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Mirco Mutti

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26 papers

2 author rows

ICML Conference 2025 Conference Paper

A Classification View on Meta Learning Bandits

Mirco Mutti
Jeongyeol Kwon
Shie Mannor
Aviv Tamar

Contextual multi-armed bandits are a popular choice to model sequential decision-making. E. g. , in a healthcare application we may perform various tests to asses a patient condition (exploration) and then decide on the best treatment to give (exploitation). When human design strategies, they aim for the exploration to be fast, since the patient’s health is at stake, and easy to interpret for a physician overseeing the process. However, common bandit algorithms are nothing like that: The regret caused by exploration scales with $\sqrt{H}$ over $H$ rounds and decision strategies are based on opaque statistical considerations. In this paper, we use an original classification view to meta learn interpretable and fast exploration plans for a fixed collection of bandits $\mathbb{M}$. The plan is prescribed by an interpretable decision tree probing decisions’ payoff to classify the test bandit. The test regret of the plan in the stochastic and contextual setting scales with $O (\lambda^{-2} C_{\lambda} (\mathbb{M}) \log^2 (MH))$, being $M$ the size of $\mathbb{M}$, $\lambda$ a separation parameter over the bandits, and $C_\lambda (\mathbb{M})$ a novel classification-coefficient that fundamentally links meta learning bandits with classification. Through a nearly matching lower bound, we show that $C_\lambda (\mathbb{M})$ inherently captures the complexity of the setting.

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EWRL Workshop 2025 Workshop Paper

A Classification View on Meta Learning Bandits

Mirco Mutti
Jeongyeol Kwon
Shie Mannor
Aviv Tamar

Contextual multi-armed bandits are a popular choice to model sequential decision-making. E. g. , in a healthcare application we may perform various tests to asses a patient condition (exploration) and then decide on the best treatment to give (exploitation). When humans design strategies, they aim for the exploration to be fast, since the patient's health is at stake, and easy to interpret for a physician overseeing the process. However, common bandit algorithms are nothing like that: The regret caused by exploration scales with $\sqrt{H}$ over $H$ rounds and decision strategies are based on opaque statistical considerations. In this paper, we use an original classification view to meta learn interpretable and fast exploration plans for a fixed collection of bandits $\mathbb{M}$. The plan is prescribed by an interpretable decision tree probing decisions' payoff to classify the test bandit. The test regret of the plan in the stochastic and contextual setting scales with $O (\lambda^{-2} C_{\lambda} (\mathbb{M}) \log^2 (MH))$, being $M$ the size of $\mathbb{M}$, $\lambda$ a separation parameter over the bandits, and $C_\lambda (\mathbb{M})$ a novel classification-coefficient that fundamentally links meta learning bandits with classification. Through a nearly matching lower bound, we show that $C_\lambda (\mathbb{M})$ inherently captures the complexity of the setting.

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ICLR Conference 2025 Conference Paper

A Theoretical Framework for Partially-Observed Reward States in RLHF

Chinmaya Kausik
Mirco Mutti
Aldo Pacchiano
Ambuj Tewari

The growing deployment of reinforcement learning from human feedback (RLHF) calls for a deeper theoretical investigation of its underlying models. The prevalent models of RLHF do not account for neuroscience-backed, partially-observed "internal states'' that can affect human feedback, nor do they accommodate intermediate feedback during an interaction. Both of these can be instrumental in speeding up learning and improving alignment. To address these limitations, we model RLHF as reinforcement learning with partially observed reward-states (PORRL). We accommodate two kinds of feedback — cardinal and dueling feedback. We first demonstrate that PORRL subsumes a wide class of RL problems, including traditional RL, RLHF, and reward machines. For cardinal feedback, we present two model-based methods (POR-UCRL, POR-UCBVI). We give both cardinal regret and sample complexity guarantees for the methods, showing that they improve over naive history-summarization. We then discuss the benefits of a model-free method like GOLF with naive history-summarization in settings with recursive internal states and dense intermediate feedback. For this purpose, we define a new history aware version of the Bellman-eluder dimension and give a new guarantee for GOLF in our setting, which can be exponentially sharper in illustrative examples. For dueling feedback, we show that a naive reduction to cardinal feedback fails to achieve sublinear dueling regret. We then present the first explicit reduction that converts guarantees for cardinal regret to dueling regret. In both feedback settings, we show that our models and guarantees generalize and extend existing ones.

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NeurIPS Conference 2025 Conference Paper

Blindfolded Experts Generalize Better: Insights from Robotic Manipulation and Videogames

Ev Zisselman
Mirco Mutti
Shelly Francis-Meretzki
Elisei Shafer
Aviv Tamar

Behavioral cloning is a simple yet effective technique for learning sequential decision-making from demonstrations. Recently, it has gained prominence as the core of foundation models for the physical world, where achieving generalization requires countless demonstrations of a multitude of tasks. Typically, a human expert with full information on the task demonstrates a (nearly) optimal behavior. In this paper, we propose to hide some of the task's information from the demonstrator. This ``blindfolded'' expert is compelled to employ non-trivial *exploration* to solve the task. We show that cloning the blindfolded expert generalizes better to unseen tasks than its fully-informed counterpart. We conduct experiments of real-world robot peg insertion tasks with (limited) human demonstrations, alongside videogames from the Procgen benchmark. Additionally, we support our findings with theoretical analysis, which confirms that the generalization error scales with $\sqrt{I/m}$, where $I$ measures the amount of task information available to the demonstrator, and $m$ is the number of demonstrated tasks. Both theory and practice indicate that cloning blindfolded experts generalizes better with fewer demonstrated tasks. Project page with videos and code: [https: //sites. google. com/view/blindfoldedexperts/home](https: //sites. google. com/view/blindfoldedexperts/home)

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ICML Conference 2025 Conference Paper

Enhancing Diversity In Parallel Agents: A Maximum State Entropy Exploration Story

Vincenzo De Paola
Riccardo Zamboni
Mirco Mutti
Marcello Restelli

Parallel data collection has redefined Reinforcement Learning (RL), unlocking unprecedented efficiency and powering breakthroughs in large-scale real-world applications. In this paradigm, $N$ identical agents operate in $N$ replicas of an environment simulator, accelerating data collection by a factor of $N$. A critical question arises: Does specializing the policies of the parallel agents hold the key to surpass the $N$ factor acceleration? In this paper, we introduce a novel learning framework that maximizes the entropy of collected data in a parallel setting. Our approach carefully balances the entropy of individual agents with inter-agent diversity, effectively minimizing redundancies. The latter idea is implemented with a centralized policy gradient method, which shows promise when evaluated empirically against systems of identical agents, as well as synergy with batch RL techniques that can exploit data diversity. Finally, we provide an original concentration analysis that shows faster rates for specialized parallel sampling distributions, which supports our methodology and may be of independent interest.

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NeurIPS Conference 2025 Conference Paper

State Entropy Regularization for Robust Reinforcement Learning

Yonatan Ashlag
Uri Koren
Mirco Mutti
Esther Derman
Pierre-Luc Bacon
Shie Mannor

State entropy regularization has empirically shown better exploration and sample complexity in reinforcement learning (RL). However, its theoretical guarantees have not been studied. In this paper, we show that state entropy regularization improves robustness to structured and spatially correlated perturbations. These types of variation are common in transfer learning but often overlooked by standard robust RL methods, which typically focus on small, uncorrelated changes. We provide a comprehensive characterization of these robustness properties, including formal guarantees under reward and transition uncertainty, as well as settings where the method performs poorly. Much of our analysis contrasts state entropy with the widely used policy entropy regularization, highlighting their different benefits. Finally, from a practical standpoint, we illustrate that compared with policy entropy, the robustness advantages of state entropy are more sensitive to the number of rollouts used for policy evaluation.

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NeurIPS Conference 2025 Conference Paper

Towards Principled Unsupervised Multi-Agent Reinforcement Learning

Riccardo Zamboni
Mirco Mutti
Marcello Restelli

In reinforcement learning, we typically refer to unsupervised pre-training when we aim to pre-train a policy without a priori access to the task specification, i. e. , rewards, to be later employed for efficient learning of downstream tasks. In single-agent settings, the problem has been extensively studied and mostly understood. A popular approach casts the unsupervised objective as maximizing the entropy of the state distribution induced by the agent's policy, from which principles and methods follow. In contrast, little is known about state entropy maximization in multi-agent settings, which are ubiquitous in the real world. What are the pros and cons of alternative problem formulations in this setting? How hard is the problem in theory, how can we solve it in practice? In this paper, we address these questions by first characterizing those alternative formulations and highlighting how the problem, even when tractable in theory, is non-trivial in practice. Then, we present a scalable, decentralized, trust-region policy search algorithm to address the problem in practical settings. Finally, we provide numerical validations to both corroborate the theoretical findings and pave the way for unsupervised multi-agent reinforcement learning via state entropy maximization in challenging domains, showing that optimizing for a specific objective, namely mixture entropy, provides an excellent trade-off between tractability and performances.

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ICLR Conference 2024 Conference Paper

Exploiting Causal Graph Priors with Posterior Sampling for Reinforcement Learning

Mirco Mutti
Riccardo De Santi
Marcello Restelli
Alexander Marx 0001
Giorgia Ramponi

Posterior sampling allows exploitation of prior knowledge on the environment's transition dynamics to improve the sample efficiency of reinforcement learning. The prior is typically specified as a class of parametric distributions, the design of which can be cumbersome in practice, often resulting in the choice of uninformative priors. In this work, we propose a novel posterior sampling approach in which the prior is given as a (partial) causal graph over the environment's variables. The latter is often more natural to design, such as listing known causal dependencies between biometric features in a medical treatment study. Specifically, we propose a hierarchical Bayesian procedure, called C-PSRL, simultaneously learning the full causal graph at the higher level and the parameters of the resulting factored dynamics at the lower level. We provide an analysis of the Bayesian regret of C-PSRL that explicitly connects the regret rate with the degree of prior knowledge. Our numerical evaluation conducted in illustrative domains confirms that C-PSRL strongly improves the efficiency of posterior sampling with an uninformative prior while performing close to posterior sampling with the full causal graph.

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ICML Conference 2024 Conference Paper

Geometric Active Exploration in Markov Decision Processes: the Benefit of Abstraction

Riccardo De Santi
Federico Arangath Joseph
Noah Liniger
Mirco Mutti
Andreas Krause 0001

How can a scientist use a Reinforcement Learning (RL) algorithm to design experiments over a dynamical system’s state space? In the case of finite and Markovian systems, an area called Active Exploration (AE) relaxes the optimization problem of experiments design into Convex RL, a generalization of RL admitting a wider notion of reward. Unfortunately, this framework is currently not scalable and the potential of AE is hindered by the vastness of experiments spaces typical of scientific discovery applications. However, these spaces are often endowed with natural geometries, e. g. , permutation invariance in molecular design, that an agent could leverage to improve the statistical and computational efficiency of AE. To achieve this, we bridge AE and MDP homomorphisms, which offer a way to exploit known geometric structures via abstraction. Towards this goal, we make two fundamental contributions: we extend MDP homomorphisms formalism to Convex RL, and we present, to the best of our knowledge, the first analysis that formally captures the benefit of abstraction via homomorphisms on sample efficiency. Ultimately, we propose the Geometric Active Exploration (GAE) algorithm, which we analyse theoretically and experimentally in environments motivated by problems in scientific discovery.

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NeurIPS Conference 2024 Conference Paper

How does Inverse RL Scale to Large State Spaces? A Provably Efficient Approach

Filippo Lazzati
Mirco Mutti
Alberto Maria Metelli

In online Inverse Reinforcement Learning (IRL), the learner can collect samples about the dynamics of the environment to improve itsestimate of the reward function. Since IRL suffers from identifiability issues, many theoretical works on online IRL focus on estimating the entire set of rewards that explain the demonstrations, named the feasible reward set. However, none of the algorithms available in literature can scale to problems with large state spaces. In this paper, we focus on the online IRL problem in Linear Markov DecisionProcesses (MDPs). We show that the structure offered by Linear MDPs is not sufficient for efficiently estimating the feasible set when the state space is large. As a consequence, we introduce the novel framework of rewards compatibility, which generalizes the notion of feasible set, and we develop CATY-IRL, a sample efficient algorithm whose complexity is independent of the size of the state space in Linear MDPs. When restricted to the tabular setting, we demonstrate that CATY-IRL is minimax optimal up to logarithmic factors. As a by-product, we show that Reward-Free Exploration (RFE) enjoys the same worst-case rate, improving over the state-of-the-art lower bound. Finally, we devise a unifying framework for IRL and RFE that may be of independent interest.

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ICML Conference 2024 Conference Paper

How to Explore with Belief: State Entropy Maximization in POMDPs

Riccardo Zamboni
Duilio Cirino
Marcello Restelli
Mirco Mutti

Recent works have studied state entropy maximization in reinforcement learning, in which the agent’s objective is to learn a policy inducing high entropy over states visitation (Hazan et al. , 2019). They typically assume full observability of the state of the system, so that the entropy of the observations is maximized. In practice, the agent may only get partial observations, e. g. , a robot perceiving the state of a physical space through proximity sensors and cameras. A significant mismatch between the entropy over observations and true states of the system can arise in those settings. In this paper, we address the problem of entropy maximization over the true states with a decision policy conditioned on partial observations only. The latter is a generalization of POMDPs, which is intractable in general. We develop a memory and computationally efficient policy gradient method to address a first-order relaxation of the objective defined on belief states, providing various formal characterizations of approximation gaps, the optimization landscape, and the hallucination problem. This paper aims to generalize state entropy maximization to more realistic domains that meet the challenges of applications.

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ICML Conference 2024 Conference Paper

Offline Inverse RL: New Solution Concepts and Provably Efficient Algorithms

Filippo Lazzati
Mirco Mutti
Alberto Maria Metelli

Inverse reinforcement learning (IRL) aims to recover the reward function of an expert agent from demonstrations of behavior. It is well-known that the IRL problem is fundamentally ill-posed, i. e. , many reward functions can explain the demonstrations. For this reason, IRL has been recently reframed in terms of estimating the feasible reward set (Metelli et al. , 2021), thus, postponing the selection of a single reward. However, so far, the available formulations and algorithmic solutions have been proposed and analyzed mainly for the online setting, where the learner can interact with the environment and query the expert at will. This is clearly unrealistic in most practical applications, where the availability of an offline dataset is a much more common scenario. In this paper, we introduce a novel notion of feasible reward set capturing the opportunities and limitations of the offline setting and we analyze the complexity of its estimation. This requires the introduction an original learning framework that copes with the intrinsic difficulty of the setting, for which data coverage is not under control. Then, we propose two computationally and statistically efficient algorithms, IRLO and PIRLO, for addressing the problem. In particular, the latter adopts a specific form of pessimism to enforce the novel, desirable property of inclusion monotonicity of the delivered feasible set. With this work, we aim to provide a panorama of the challenges of the offline IRL problem and how they can be fruitfully addressed.

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ICML Conference 2024 Conference Paper

Test-Time Regret Minimization in Meta Reinforcement Learning

Mirco Mutti
Aviv Tamar

Meta reinforcement learning sets a distribution over a set of tasks on which the agent can train at will, then is asked to learn an optimal policy for any test task efficiently. In this paper, we consider a finite set of tasks modeled through Markov decision processes with various dynamics. We assume to have endured a long training phase, from which the set of tasks is perfectly recovered, and we focus on regret minimization against the optimal policy in the unknown test task. Under a separation condition that states the existence of a state-action pair revealing a task against another, Chen et al. (2022) show that $O(M^2 \log(H))$ regret can be achieved, where $M, H$ are the number of tasks in the set and test episodes, respectively. In our first contribution, we demonstrate that the latter rate is nearly optimal by developing a novel lower bound for test-time regret minimization under separation, showing that a linear dependence with $M$ is unavoidable. Then, we present a family of stronger yet reasonable assumptions beyond separation, which we call strong identifiability, enabling algorithms achieving fast rates $\log (H)$ and sublinear dependence with $M$ simultaneously. Our paper provides a new understanding of the statistical barriers of test-time regret minimization and when fast rates can be achieved.

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RLC Conference 2024 Conference Paper

The Limits of Pure Exploration in POMDPs: When the Observation Entropy is Enough

Riccardo Zamboni
Duilio Cirino
Marcello Restelli
Mirco Mutti

The problem of pure exploration in Markov decision processes has been cast as maximizing the entropy over the state distribution induced by the agent's policy, an objective that has been extensively studied. However, little attention has been dedicated to state entropy maximization under partial observability, despite the latter being ubiquitous in applications, e. g. , finance and robotics, in which the agent only receives noisy observations of the true state governing the system's dynamics. How can we address state entropy maximization in those domains? In this paper, we study the simple approach of maximizing the entropy over observations in place of true latent states. First, we provide lower and upper bounds to the approximation of the true state entropy that only depends on some properties of the observation function. Then, we show how knowledge of the latter can be exploited to compute a principled regularization of the observation entropy to improve performance. With this work, we provide both a flexible approach to bring advances in state entropy maximization to the POMDP setting and a theoretical characterization of its intrinsic limits.

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RLJ Journal 2024 Journal Article

The Limits of Pure Exploration in POMDPs: When the Observation Entropy is Enough

Riccardo Zamboni
Duilio Cirino
Marcello Restelli
Mirco Mutti

The problem of pure exploration in Markov decision processes has been cast as maximizing the entropy over the state distribution induced by the agent's policy, an objective that has been extensively studied. However, little attention has been dedicated to state entropy maximization under partial observability, despite the latter being ubiquitous in applications, e.g., finance and robotics, in which the agent only receives noisy observations of the true state governing the system's dynamics. How can we address state entropy maximization in those domains? In this paper, we study the simple approach of maximizing the entropy over observations in place of true latent states. First, we provide lower and upper bounds to the approximation of the true state entropy that only depends on some properties of the observation function. Then, we show how knowledge of the latter can be exploited to compute a principled regularization of the observation entropy to improve performance. With this work, we provide both a flexible approach to bring advances in state entropy maximization to the POMDP setting and a theoretical characterization of its intrinsic limits.

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JMLR Journal 2023 Journal Article

Convex Reinforcement Learning in Finite Trials

Mirco Mutti
Riccardo De Santi
Piersilvio De Bartolomeis
Marcello Restelli

Convex Reinforcement Learning (RL) is a recently introduced framework that generalizes the standard RL objective to any convex (or concave) function of the state distribution induced by the agent's policy. This framework subsumes several applications of practical interest, such as pure exploration, imitation learning, and risk-averse RL, among others. However, the previous convex RL literature implicitly evaluates the agent's performance over infinite realizations (or trials), while most of the applications require excellent performance over a handful, or even just one, trials. To meet this practical demand, we formulate convex RL in finite trials, where the objective is any convex function of the empirical state distribution computed over a finite number of realizations. In this paper, we provide a comprehensive theoretical study of the setting, which includes an analysis of the importance of non-Markovian policies to achieve optimality, as well as a characterization of the computational and statistical complexity of the problem in various configurations. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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EWRL Workshop 2023 Workshop Paper

Exploiting Causal Graph Priors with Posterior Sampling for Reinforcement Learning

Mirco Mutti
Riccardo De Santi
Marcello Restelli
Alexander Marx
Giorgia Ramponi

Posterior sampling allows the exploitation of prior knowledge of the environment's transition dynamics to improve the sample efficiency of reinforcement learning. The prior is typically specified as a class of parametric distributions, a task that can be cumbersome in practice, often resulting in the choice of uninformative priors. In this work, we propose a novel posterior sampling approach in which the prior is given as a (partial) causal graph over the environment's variables. The latter is often more natural to design, such as listing known causal dependencies between biometric features in a medical treatment study. Specifically, we propose a hierarchical Bayesian procedure, called C-PSRL, simultaneously learning the full causal graph at the higher level and the parameters of the resulting factored dynamics at the lower level. For this procedure, we provide an analysis of its Bayesian regret, which explicitly connects the regret rate with the degree of prior knowledge. Our numerical evaluation conducted in illustrative domains confirms that C-PSRL strongly improves the efficiency of posterior sampling with an uninformative prior while performing close to posterior sampling with the full causal graph.

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NeurIPS Conference 2023 Conference Paper

Persuading Farsighted Receivers in MDPs: the Power of Honesty

Martino Bernasconi
Matteo Castiglioni
Alberto Marchesi
Mirco Mutti

Bayesian persuasion studies the problem faced by an informed sender who strategically discloses information to influence the behavior of an uninformed receiver. Recently, a growing attention has been devoted to settings where the sender and the receiver interact sequentially, in which the receiver's decision-making problem is usually modeled as a Markov decision process (MDP). However, the literature focuses on computing optimal information-revelation policies (a. k. a. signaling schemes) under the restrictive assumption that the receiver acts myopically, selecting actions to maximize the one-step utility and disregarding future rewards. This is justified by the fact that, when the receiver is farsighted and thus considers future rewards, finding an optimal Markovian signaling scheme is NP-hard. In this paper, we show that Markovian signaling schemes do not constitute the "right" class of policies. Indeed, differently from most of the MDPs settings, we show that Markovian signaling schemes are not optimal, and general history-dependent signaling schemes should be considered. Moreover, we also show that history-dependent signaling schemes circumvent the negative complexity results affecting Markovian signaling schemes. Formally, we design an algorithm that computes an optimal and $\epsilon$-persuasive history-dependent signaling scheme in time polynomial in ${1}/{\epsilon}$ and in the instance size. The crucial challenge is that general history-dependent signaling schemes cannot be represented in polynomial space. Nevertheless, we introduce a convenient subclass of history-dependent signaling schemes, called promise-form, which are as powerful as general history-dependent ones and efficiently representable. Intuitively, promise-form signaling schemes compactly encode histories in the form of honest promises on future receiver's rewards.

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AAAI Conference 2023 Conference Paper

Provably Efficient Causal Model-Based Reinforcement Learning for Systematic Generalization

Mirco Mutti
Riccardo De Santi
Emanuele Rossi
Juan Felipe Calderon
Michael Bronstein
Marcello Restelli

In the sequential decision making setting, an agent aims to achieve systematic generalization over a large, possibly infinite, set of environments. Such environments are modeled as discrete Markov decision processes with both states and actions represented through a feature vector. The underlying structure of the environments allows the transition dynamics to be factored into two components: one that is environment-specific and another that is shared. Consider a set of environments that share the laws of motion as an example. In this setting, the agent can take a finite amount of reward-free interactions from a subset of these environments. The agent then must be able to approximately solve any planning task defined over any environment in the original set, relying on the above interactions only. Can we design a provably efficient algorithm that achieves this ambitious goal of systematic generalization? In this paper, we give a partially positive answer to this question. First, we provide a tractable formulation of systematic generalization by employing a causal viewpoint. Then, under specific structural assumptions, we provide a simple learning algorithm that guarantees any desired planning error up to an unavoidable sub-optimality term, while showcasing a polynomial sample complexity.

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NeurIPS Conference 2022 Conference Paper

Challenging Common Assumptions in Convex Reinforcement Learning

Mirco Mutti
Riccardo De Santi
Piersilvio De Bartolomeis
Marcello Restelli

The classic Reinforcement Learning (RL) formulation concerns the maximization of a scalar reward function. More recently, convex RL has been introduced to extend the RL formulation to all the objectives that are convex functions of the state distribution induced by a policy. Notably, convex RL covers several relevant applications that do not fall into the scalar formulation, including imitation learning, risk-averse RL, and pure exploration. In classic RL, it is common to optimize an infinite trials objective, which accounts for the state distribution instead of the empirical state visitation frequencies, even though the actual number of trajectories is always finite in practice. This is theoretically sound since the infinite trials and finite trials objectives are equivalent and thus lead to the same optimal policy. In this paper, we show that this hidden assumption does not hold in convex RL. In particular, we prove that erroneously optimizing the infinite trials objective in place of the actual finite trials one, as it is usually done, can lead to a significant approximation error. Since the finite trials setting is the default in both simulated and real-world RL, we believe shedding light on this issue will lead to better approaches and methodologies for convex RL, impacting relevant research areas such as imitation learning, risk-averse RL, and pure exploration among others.

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ICML Conference 2022 Conference Paper

The Importance of Non-Markovianity in Maximum State Entropy Exploration

Mirco Mutti
Riccardo De Santi
Marcello Restelli

In the maximum state entropy exploration framework, an agent interacts with a reward-free environment to learn a policy that maximizes the entropy of the expected state visitations it is inducing. Hazan et al. (2019) noted that the class of Markovian stochastic policies is sufficient for the maximum state entropy objective, and exploiting non-Markovianity is generally considered pointless in this setting. In this paper, we argue that non-Markovianity is instead paramount for maximum state entropy exploration in a finite-sample regime. Especially, we recast the objective to target the expected entropy of the induced state visitations in a single trial. Then, we show that the class of non-Markovian deterministic policies is sufficient for the introduced objective, while Markovian policies suffer non-zero regret in general. However, we prove that the problem of finding an optimal non-Markovian policy is NP-hard. Despite this negative result, we discuss avenues to address the problem in a tractable way and how non-Markovian exploration could benefit the sample efficiency of online reinforcement learning in future works.

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AAAI Conference 2022 Conference Paper

Unsupervised Reinforcement Learning in Multiple Environments

Mirco Mutti
Mattia Mancassola
Marcello Restelli

Several recent works have been dedicated to unsupervised reinforcement learning in a single environment, in which a policy is first pre-trained with unsupervised interactions, and then fine-tuned towards the optimal policy for several downstream supervised tasks defined over the same environment. Along this line, we address the problem of unsupervised reinforcement learning in a class of multiple environments, in which the policy is pre-trained with interactions from the whole class, and then fine-tuned for several tasks in any environment of the class. Notably, the problem is inherently multi-objective as we can trade off the pre-training objective between environments in many ways. In this work, we foster an exploration strategy that is sensitive to the most adverse cases within the class. Hence, we cast the exploration problem as the maximization of the mean of a critical percentile of the state visitation entropy induced by the exploration strategy over the class of environments. Then, we present a policy gradient algorithm, αMEPOL, to optimize the introduced objective through mediated interactions with the class. Finally, we empirically demonstrate the ability of the algorithm in learning to explore challenging classes of continuous environments and we show that reinforcement learning greatly benefits from the pre-trained exploration strategy w. r. t. learning from scratch.

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AAAI Conference 2021 Conference Paper

Task-Agnostic Exploration via Policy Gradient of a Non-Parametric State Entropy Estimate

Mirco Mutti
Lorenzo Pratissoli
Marcello Restelli

In a reward-free environment, what is a suitable intrinsic objective for an agent to pursue so that it can learn an optimal taskagnostic exploration policy? In this paper, we argue that the entropy of the state distribution induced by finite-horizon trajectories is a sensible target. Especially, we present a novel and practical policy-search algorithm, Maximum Entropy POLicy optimization (MEPOL), to learn a policy that maximizes a non-parametric, k-nearest neighbors estimate of the state distribution entropy. In contrast to known methods, MEPOL is completely model-free as it requires neither to estimate the state distribution of any policy nor to model transition dynamics. Then, we empirically show that MEPOL allows learning a maximum-entropy exploration policy in high-dimensional, continuous-control domains, and how this policy facilitates learning meaningful reward-based tasks downstream.

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AAAI Conference 2020 Conference Paper

An Intrinsically-Motivated Approach for Learning Highly Exploring and Fast Mixing Policies

Mirco Mutti
Marcello Restelli

What is a good exploration strategy for an agent that interacts with an environment in the absence of external rewards? Ideally, we would like to get a policy driving towards a uniform state-action visitation (highly exploring) in a minimum number of steps (fast mixing), in order to ease efﬁcient learning of any goal-conditioned policy later on. Unfortunately, it is remarkably arduous to directly learn an optimal policy of this nature. In this paper, we propose a novel surrogate objective for learning highly exploring and fast mixing policies, which focuses on maximizing a lower bound to the entropy of the steady-state distribution induced by the policy. In particular, we introduce three novel lower bounds, that lead to as many optimization problems, that tradeoff the theoretical guarantees with computational complexity. Then, we present a modelbased reinforcement learning algorithm, IDE3 AL, to learn an optimal policy according to the introduced objective. Finally, we provide an empirical evaluation of this algorithm on a set of hard-exploration tasks.

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ICML Conference 2018 Conference Paper

Configurable Markov Decision Processes

Alberto Maria Metelli
Mirco Mutti
Marcello Restelli

In many real-world problems, there is the possibility to configure, to a limited extent, some environmental parameters to improve the performance of a learning agent. In this paper, we propose a novel framework, Configurable Markov Decision Processes (Conf-MDPs), to model this new type of interaction with the environment. Furthermore, we provide a new learning algorithm, Safe Policy-Model Iteration (SPMI), to jointly and adaptively optimize the policy and the environment configuration. After having introduced our approach and derived some theoretical results, we present the experimental evaluation in two explicative problems to show the benefits of the environment configurability on the performance of the learned policy.

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EWRL Workshop 2018 Workshop Paper

Configurable Markov Decision Processes

Alberto Maria Metelli
Mirco Mutti
Marcello Restelli

In many real-world problems, there is the possibility to configure, to a limited extent, some environmental parameters to improve the performance of a learning agent. In this paper, we propose a novel framework, Configurable Markov Decision Processes (Conf-MDPs), to model this new type of interaction with the environment. Furthermore, we provide a new learning algorithm, Safe Policy-Model Iteration (SPMI), to jointly and adaptively optimize the policy and the environment configuration. After having introduced our approach, we present the experimental evaluation in two explicative problems to show the benefits of the environment configurability on the performance of the learned policy.

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