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Mark Rowland 0001

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26 papers

1 author row

ICML Conference 2025 Conference Paper

Categorical Distributional Reinforcement Learning with Kullback-Leibler Divergence: Convergence and Asymptotics

Tyler Kastner
Mark Rowland 0001
Yunhao Tang
Murat A. Erdogdu
Amir Massoud Farahmand

We study the problem of distributional reinforcement learning using categorical parametrisations and a KL divergence loss. Previous work analyzing categorical distributional RL has done so using a Cramér distance-based loss, simplifying the analysis but creating a theory-practice gap. We introduce a preconditioned version of the algorithm, and prove that it is guaranteed to converge. We further derive the asymptotic variance of the categorical estimates under different learning rate regimes, and compare to that of classical reinforcement learning. We finally empirically validate our theoretical results and perform an empirical investigation into the relative strengths of using KL losses, and derive a number of actionable insights for practitioners.

ICML Conference 2024 Conference Paper

A Distributional Analogue to the Successor Representation

Harley Wiltzer
Jesse Farebrother
Arthur Gretton
Yunhao Tang
André Barreto 0001
Will Dabney
Marc G. Bellemare
Mark Rowland 0001

This paper contributes a new approach for distributional reinforcement learning which elucidates a clean separation of transition structure and reward in the learning process. Analogous to how the successor representation (SR) describes the expected consequences of behaving according to a given policy, our distributional successor measure (SM) describes the distributional consequences of this behaviour. We formulate the distributional SM as a distribution over distributions and provide theory connecting it with distributional and model-based reinforcement learning. Moreover, we propose an algorithm that learns the distributional SM from data by minimizing a two-level maximum mean discrepancy. Key to our method are a number of algorithmic techniques that are independently valuable for learning generative models of state. As an illustration of the usefulness of the distributional SM, we show that it enables zero-shot risk-sensitive policy evaluation in a way that was not previously possible.

ICML Conference 2024 Conference Paper

Distributional Bellman Operators over Mean Embeddings

Li Kevin Wenliang
Grégoire Delétang
Matthew Aitchison
Marcus Hutter
Anian Ruoss
Arthur Gretton
Mark Rowland 0001

We propose a novel algorithmic framework for distributional reinforcement learning, based on learning finite-dimensional mean embeddings of return distributions. The framework reveals a wide variety of new algorithms for dynamic programming and temporal-difference algorithms that rely on the sketch Bellman operator, which updates mean embeddings with simple linear-algebraic computations. We provide asymptotic convergence theory, and examine the empirical performance of the algorithms on a suite of tabular tasks. Further, we show that this approach can be straightforwardly combined with deep reinforcement learning.

ICML Conference 2024 Conference Paper

Generalized Preference Optimization: A Unified Approach to Offline Alignment

Yunhao Tang
Daniel Guo 0001
Zeyu Zheng
Daniele Calandriello
Rémi Munos
Mark Rowland 0001
Pierre Harvey Richemond
Michal Valko

Offline preference optimization allows fine-tuning large models directly from offline data, and has proved effective in recent alignment practices. We propose generalized preference optimization (GPO), a family of offline losses parameterized by a general class of convex functions. GPO enables a unified view over preference optimization, encompassing existing algorithms such as DPO, IPO and SLiC as special cases, while naturally introducing new variants. The GPO framework also sheds light on how offline algorithms enforce regularization, through the design of the convex function that defines the loss. Our analysis and experiments reveal the connections and subtle differences between the offline regularization and the KL divergence regularization intended by the canonical RLHF formulation. In a controlled setting akin to Gao et al 2023, we also show that different GPO variants achieve similar trade-offs between regularization and performance, though the optimal values of hyper-parameter might differ as predicted by theory. In all, our results present new algorithmic toolkits and empirical insights to alignment practitioners.

ICML Conference 2024 Conference Paper

Human Alignment of Large Language Models through Online Preference Optimisation

Daniele Calandriello
Daniel Guo 0001
Rémi Munos
Mark Rowland 0001
Yunhao Tang
Bernardo Ávila Pires
Pierre Harvey Richemond
Charline Le Lan

Ensuring alignment of language model’s outputs with human preferences is critical to guarantee a useful, safe, and pleasant user experience. Thus, human alignment has been extensively studied recently and several methods such as Reinforcement Learning from Human Feedback (RLHF), Direct Policy Optimisation (DPO) and Sequence Likelihood Calibration (SLiC) have emerged. In this paper, our contribution is two-fold. First, we show the equivalence between two recent alignment methods, namely Identity Policy Optimisation (IPO) and Nash Mirror Descent (Nash-MD). Second, we introduce a generalisation of IPO, named IPO-MD, that leverages the regularised sampling approach proposed by Nash-MD. This equivalence may seem surprising at first sight, since IPO is an offline method whereas Nash-MD is an online method using a preference model. However, this equivalence can be proven when we consider the online version of IPO, that is when both generations are sampled by the online policy and annotated by a trained preference model. Optimising the IPO loss with such a stream of data becomes then equivalent to finding the Nash equilibrium of the preference model through self-play. Building on this equivalence, we introduce the IPO-MD algorithm that generates data with a mixture policy (between the online and reference policy) similarly as the general Nash-MD algorithm. We compare online-IPO and IPO-MD to different online versions of existing losses on preference data such as DPO and SLiC on a summarisation task.

ICML Conference 2024 Conference Paper

Nash Learning from Human Feedback

Rémi Munos
Michal Valko
Daniele Calandriello
Mohammad Gheshlaghi Azar
Mark Rowland 0001
Daniel Guo 0001
Yunhao Tang
Matthieu Geist

Reinforcement learning from human feedback (RLHF) has emerged as the main paradigm for aligning large language models (LLMs) with human preferences. Traditionally, RLHF involves the initial step of learning a reward model from pairwise human feedback, i. e. , expressed as preferences between pairs of text generations. Subsequently, the LLM’s policy is fine-tuned to maximize the reward through a reinforcement learning algorithm. In this study, we introduce an alternative pipeline for the fine-tuning of LLMs using pairwise human feedback. Our approach entails the initial learning of a pairwise preference model, which is conditioned on two inputs (instead of a single input in the case of a reward model) given a prompt, followed by the pursuit of a policy that consistently generates responses preferred over those generated by any competing policy, thus defining the Nash equilibrium of this preference model. We term this approach Nash learning from human feedback (NLHF). In the context of a tabular policy representation, we present a novel algorithmic solution, Nash-MD, founded on the principles of mirror descent. This algorithm produces a sequence of policies, with the last iteration converging to the regularized Nash equilibrium. Additionally, we explore parametric representations of policies and introduce gradient descent algorithms for deep-learning architectures. We illustrate the effectiveness of our approach by presenting experimental results on a text summarization task. We believe NLHF offers a compelling avenue for fine-tuning LLMs and enhancing the alignment of LLMs with human preferences.

ICML Conference 2023 Conference Paper

Bootstrapped Representations in Reinforcement Learning

Charline Le Lan
Stephen Tu
Mark Rowland 0001
Anna Harutyunyan
Rishabh Agarwal
Marc G. Bellemare
Will Dabney

In reinforcement learning (RL), state representations are key to dealing with large or continuous state spaces. While one of the promises of deep learning algorithms is to automatically construct features well-tuned for the task they try to solve, such a representation might not emerge from end-to-end training of deep RL agents. To mitigate this issue, auxiliary objectives are often incorporated into the learning process and help shape the learnt state representation. Bootstrapping methods are today’s method of choice to make these additional predictions. Yet, it is unclear which features these algorithms capture and how they relate to those from other auxiliary-task-based approaches. In this paper, we address this gap and provide a theoretical characterization of the state representation learnt by temporal difference learning (Sutton, 1988). Surprisingly, we find that this representation differs from the features learned by Monte Carlo and residual gradient algorithms for most transition structures of the environment in the policy evaluation setting. We describe the efficacy of these representations for policy evaluation, and use our theoretical analysis to design new auxiliary learning rules. We complement our theoretical results with an empirical comparison of these learning rules for different cumulant functions on classic domains such as the four-room domain (Sutton et al, 1999) and Mountain Car (Moore, 1990).

ICML Conference 2023 Conference Paper

DoMo-AC: Doubly Multi-step Off-policy Actor-Critic Algorithm

Yunhao Tang
Tadashi Kozuno
Mark Rowland 0001
Anna Harutyunyan
Rémi Munos
Bernardo Ávila Pires
Michal Valko

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

ICML Conference 2023 Conference Paper

Quantile Credit Assignment

Thomas Mesnard
Wenqi Chen
Alaa Saade
Yunhao Tang
Mark Rowland 0001
Theophane Weber
Clare Lyle
Audrunas Gruslys

In reinforcement learning, the credit assignment problem is to distinguish luck from skill, that is, separate the inherent randomness in the environment from the controllable effects of the agent’s actions. This paper proposes two novel algorithms, Quantile Credit Assignment (QCA) and Hindsight QCA (HQCA), which incorporate distributional value estimation to perform credit assignment. QCA uses a network that predicts the quantiles of the return distribution, whereas HQCA additionally incorporates information about the future. Both QCA and HQCA have the appealing interpretation of leveraging an estimate of the quantile level of the return (interpreted as the level of "luck") in order to derive a "luck-dependent" baseline for policy gradient methods. We show theoretically that this approach gives an unbiased policy gradient estimate that can yield significant variance reductions over a standard value estimate baseline. QCA and HQCA significantly outperform prior state-of-the-art methods on a range of extremely difficult credit assignment problems.

ICML Conference 2023 Conference Paper

The Statistical Benefits of Quantile Temporal-Difference Learning for Value Estimation

Mark Rowland 0001
Yunhao Tang
Clare Lyle
Rémi Munos
Marc G. Bellemare
Will Dabney

We study the problem of temporal-difference-based policy evaluation in reinforcement learning. In particular, we analyse the use of a distributional reinforcement learning algorithm, quantile temporal-difference learning (QTD), for this task. We reach the surprising conclusion that even if a practitioner has no interest in the return distribution beyond the mean, QTD (which learns predictions about the full distribution of returns) may offer performance superior to approaches such as classical TD learning, which predict only the mean return, even in the tabular setting.

ICML Conference 2023 Conference Paper

Understanding Self-Predictive Learning for Reinforcement Learning

Yunhao Tang
Daniel Guo 0001
Pierre Harvey Richemond
Bernardo Ávila Pires
Yash Chandak
Rémi Munos
Mark Rowland 0001
Mohammad Gheshlaghi Azar

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

ICML Conference 2023 Conference Paper

VA-learning as a more efficient alternative to Q-learning

Yunhao Tang
Rémi Munos
Mark Rowland 0001
Michal Valko

In reinforcement learning, the advantage function is critical for policy improvement, but is often extracted from a learned Q-function. A natural question is: Why not learn the advantage function directly? In this work, we introduce VA-learning, which directly learns advantage function and value function using bootstrapping, without explicit reference to Q-functions. VA-learning learns off-policy and enjoys similar theoretical guarantees as Q-learning. Thanks to the direct learning of advantage function and value function, VA-learning improves the sample efficiency over Q-learning both in tabular implementations and deep RL agents on Atari-57 games. We also identify a close connection between VA-learning and the dueling architecture, which partially explains why a simple architectural change to DQN agents tends to improve performance.

ICML Conference 2022 Conference Paper

Generalised Policy Improvement with Geometric Policy Composition

Shantanu Thakoor
Mark Rowland 0001
Diana Borsa
Will Dabney
Rémi Munos
André Barreto 0001

We introduce a method for policy improvement that interpolates between the greedy approach of value-based reinforcement learning (RL) and the full planning approach typical of model-based RL. The new method builds on the concept of a geometric horizon model (GHM, also known as a \gamma-model), which models the discounted state-visitation distribution of a given policy. We show that we can evaluate any non-Markov policy that switches between a set of base Markov policies with fixed probability by a careful composition of the base policy GHMs, without any additional learning. We can then apply generalised policy improvement (GPI) to collections of such non-Markov policies to obtain a new Markov policy that will in general outperform its precursors. We provide a thorough theoretical analysis of this approach, develop applications to transfer and standard RL, and empirically demonstrate its effectiveness over standard GPI on a challenging deep RL continuous control task. We also provide an analysis of GHM training methods, proving a novel convergence result regarding previously proposed methods and showing how to train these models stably in deep RL settings.

ICML Conference 2022 Conference Paper

Learning Dynamics and Generalization in Deep Reinforcement Learning

Clare Lyle
Mark Rowland 0001
Will Dabney
Marta Kwiatkowska
Yarin Gal

Solving a reinforcement learning (RL) problem poses two competing challenges: fitting a potentially discontinuous value function, and generalizing well to new observations. In this paper, we analyze the learning dynamics of temporal difference algorithms to gain novel insight into the tension between these two objectives. We show theoretically that temporal difference learning encourages agents to fit non-smooth components of the value function early in training, and at the same time induces the second-order effect of discouraging generalization. We corroborate these findings in deep RL agents trained on a range of environments, finding that neural networks trained using temporal difference algorithms on dense reward tasks exhibit weaker generalization between states than randomly initialized networks and networks trained with policy gradient methods. Finally, we investigate how post-training policy distillation may avoid this pitfall, and show that this approach improves generalization to novel environments in the ProcGen suite and improves robustness to input perturbations.

ICLR Conference 2022 Conference Paper

Understanding and Preventing Capacity Loss in Reinforcement Learning

Clare Lyle
Mark Rowland 0001
Will Dabney

The reinforcement learning (RL) problem is rife with sources of non-stationarity that can destabilize or inhibit learning progress. We identify a key mechanism by which this occurs in agents using neural networks as function approximators: \textit{capacity loss}, whereby networks trained to predict a sequence of target values lose their ability to quickly fit new functions over time. We demonstrate that capacity loss occurs in a broad range of RL agents and environments, and is particularly damaging to learning progress in sparse-reward tasks. We then present a simple regularizer, Initial Feature Regularization (InFeR), that mitigates this phenomenon by regressing a subspace of features towards its value at initialization, improving performance over a state-of-the-art model-free algorithm in the Atari 2600 suite. Finally, we study how this regularization affects different notions of capacity and evaluate other mechanisms by which it may improve performance.

ICML Conference 2021 Conference Paper

From Poincaré Recurrence to Convergence in Imperfect Information Games: Finding Equilibrium via Regularization

Julien Pérolat
Rémi Munos
Jean-Baptiste Lespiau
Shayegan Omidshafiei
Mark Rowland 0001
Pedro A. Ortega
Neil Burch
Thomas W. Anthony 0001

In this paper we investigate the Follow the Regularized Leader dynamics in sequential imperfect information games (IIG). We generalize existing results of Poincar{é} recurrence from normal-form games to zero-sum two-player imperfect information games and other sequential game settings. We then investigate how adapting the reward (by adding a regularization term) of the game can give strong convergence guarantees in monotone games. We continue by showing how this reward adaptation technique can be leveraged to build algorithms that converge exactly to the Nash equilibrium. Finally, we show how these insights can be directly used to build state-of-the-art model-free algorithms for zero-sum two-player Imperfect Information Games (IIG).

ICML Conference 2021 Conference Paper

Revisiting Peng's Q(λ) for Modern Reinforcement Learning

Tadashi Kozuno
Yunhao Tang
Mark Rowland 0001
Rémi Munos
Steven Kapturowski
Will Dabney
Michal Valko
David Abel

Off-policy multi-step reinforcement learning algorithms consist of conservative and non-conservative algorithms: the former actively cut traces, whereas the latter do not. Recently, Munos et al. (2016) proved the convergence of conservative algorithms to an optimal Q-function. In contrast, non-conservative algorithms are thought to be unsafe and have a limited or no theoretical guarantee. Nonetheless, recent studies have shown that non-conservative algorithms empirically outperform conservative ones. Motivated by the empirical results and the lack of theory, we carry out theoretical analyses of Peng’s Q($\lambda$), a representative example of non-conservative algorithms. We prove that \emph{it also converges to an optimal policy} provided that the behavior policy slowly tracks a greedy policy in a way similar to conservative policy iteration. Such a result has been conjectured to be true but has not been proven. We also experiment with Peng’s Q($\lambda$) in complex continuous control tasks, confirming that Peng’s Q($\lambda$) often outperforms conservative algorithms despite its simplicity. These results indicate that Peng’s Q($\lambda$), which was thought to be unsafe, is a theoretically-sound and practically effective algorithm.

ICML Conference 2021 Conference Paper

Taylor Expansion of Discount Factors

Yunhao Tang
Mark Rowland 0001
Rémi Munos
Michal Valko

In practical reinforcement learning (RL), the discount factor used for estimating value functions often differs from that used for defining the evaluation objective. In this work, we study the effect that this discrepancy of discount factors has during learning, and discover a family of objectives that interpolate value functions of two distinct discount factors. Our analysis suggests new ways for estimating value functions and performing policy optimization updates, which demonstrate empirical performance gains. This framework also leads to new insights on commonly-used deep RL heuristic modifications to policy optimization algorithms.

ICLR Conference 2020 Conference Paper

A Generalized Training Approach for Multiagent Learning

Paul Muller
Shayegan Omidshafiei
Mark Rowland 0001
Karl Tuyls
Julien Pérolat
Siqi Liu 0002
Daniel Hennes
Luke Marris

This paper investigates a population-based training regime based on game-theoretic principles called Policy-Spaced Response Oracles (PSRO). PSRO is general in the sense that it (1) encompasses well-known algorithms such as fictitious play and double oracle as special cases, and (2) in principle applies to general-sum, many-player games. Despite this, prior studies of PSRO have been focused on two-player zero-sum games, a regime where in Nash equilibria are tractably computable. In moving from two-player zero-sum games to more general settings, computation of Nash equilibria quickly becomes infeasible. Here, we extend the theoretical underpinnings of PSRO by considering an alternative solution concept, α-Rank, which is unique (thus faces no equilibrium selection issues, unlike Nash) and applies readily to general-sum, many-player settings. We establish convergence guarantees in several games classes, and identify links between Nash equilibria and α-Rank. We demonstrate the competitive performance of α-Rank-based PSRO against an exact Nash solver-based PSRO in 2-player Kuhn and Leduc Poker. We then go beyond the reach of prior PSRO applications by considering 3- to 5-player poker games, yielding instances where α-Rank achieves faster convergence than approximate Nash solvers, thus establishing it as a favorable general games solver. We also carry out an initial empirical validation in MuJoCo soccer, illustrating the feasibility of the proposed approach in another complex domain.

ICML Conference 2020 Conference Paper

Fast computation of Nash Equilibria in Imperfect Information Games

Rémi Munos
Julien Pérolat
Jean-Baptiste Lespiau
Mark Rowland 0001
Bart De Vylder
Marc Lanctot
Finbarr Timbers
Daniel Hennes

We introduce and analyze a class of algorithms, called Mirror Ascent against an Improved Opponent (MAIO), for computing Nash equilibria in two-player zero-sum games, both in normal form and in sequential form with imperfect information. These algorithms update the policy of each player with a mirror-ascent step to maximize the value of playing against an improved opponent. An improved opponent can be a best response, a greedy policy, a policy improved by policy gradient, or by any other reinforcement learning or search techniques. We establish a convergence result of the last iterate to the set of Nash equilibria and show that the speed of convergence depends on the amount of improvement offered by these improved policies. In addition, we show that under some condition, if we use a best response as improved policy, then an exponential convergence rate is achieved.

ICML Conference 2020 Conference Paper

Revisiting Fundamentals of Experience Replay

Liam Fedus
Prajit Ramachandran
Rishabh Agarwal
Yoshua Bengio
Hugo Larochelle
Mark Rowland 0001
Will Dabney

Experience replay is central to off-policy algorithms in deep reinforcement learning (RL), but there remain significant gaps in our understanding. We therefore present a systematic and extensive analysis of experience replay in Q-learning methods, focusing on two fundamental properties: the replay capacity and the ratio of learning updates to experience collected (replay ratio). Our additive and ablative studies upend conventional wisdom around experience replay {—} greater capacity is found to substantially increase the performance of certain algorithms, while leaving others unaffected. Counterintuitively we show that theoretically ungrounded, uncorrected n-step returns are uniquely beneficial while other techniques confer limited benefit for sifting through larger memory. Separately, by directly controlling the replay ratio we contextualize previous observations in the literature and empirically measure its importance across a variety of deep RL algorithms. Finally, we conclude by testing a set of hypotheses on the nature of these performance benefits.

ICML Conference 2019 Conference Paper

Statistics and Samples in Distributional Reinforcement Learning

Mark Rowland 0001
Robert Dadashi
Saurabh Kumar 0004
Rémi Munos
Marc G. Bellemare
Will Dabney

We present a unifying framework for designing and analysing distributional reinforcement learning (DRL) algorithms in terms of recursively estimating statistics of the return distribution. Our key insight is that DRL algorithms can be decomposed as the combination of some statistical estimator and a method for imputing a return distribution consistent with that set of statistics. With this new understanding, we are able to provide improved analyses of existing DRL algorithms as well as construct a new algorithm (EDRL) based upon estimation of the expectiles of the return distribution. We compare EDRL with existing methods on a variety of MDPs to illustrate concrete aspects of our analysis, and develop a deep RL variant of the algorithm, ER-DQN, which we evaluate on the Atari-57 suite of games.

ICML Conference 2019 Conference Paper

Unifying Orthogonal Monte Carlo Methods

Krzysztof Choromanski
Mark Rowland 0001
Wenyu Chen 0003
Adrian Weller

Many machine learning methods making use of Monte Carlo sampling in vector spaces have been shown to be improved by conditioning samples to be mutually orthogonal. Exact orthogonal coupling of samples is computationally intensive, hence approximate methods have been of great interest. In this paper, we present a unifying perspective of many approximate methods by considering Givens transformations, propose new approximate methods based on this framework, and demonstrate the ﬁrst statistical guarantees for families of approximate methods in kernel approximation. We provide extensive empirical evaluations with guidance for practitioners.

ICML Conference 2018 Conference Paper

Structured Evolution with Compact Architectures for Scalable Policy Optimization

Krzysztof Choromanski
Mark Rowland 0001
Vikas Sindhwani
Richard E. Turner
Adrian Weller

We present a new method of blackbox optimization via gradient approximation with the use of structured random orthogonal matrices, providing more accurate estimators than baselines and with provable theoretical guarantees. We show that this algorithm can be successfully applied to learn better quality compact policies than those using standard gradient estimation techniques. The compact policies we learn have several advantages over unstructured ones, including faster training algorithms and faster inference. These benefits are important when the policy is deployed on real hardware with limited resources. Further, compact policies provide more scalable architectures for derivative-free optimization (DFO) in high-dimensional spaces. We show that most robotics tasks from the OpenAI Gym can be solved using neural networks with less than 300 parameters, with almost linear time complexity of the inference phase, with up to 13x fewer parameters relative to the Evolution Strategies (ES) algorithm introduced by Salimans et al. (2017). We do not need heuristics such as fitness shaping to learn good quality policies, resulting in a simple and theoretically motivated training mechanism.

ICML Conference 2017 Conference Paper

Magnetic Hamiltonian Monte Carlo

Nilesh Tripuraneni
Mark Rowland 0001
Zoubin Ghahramani
Richard E. Turner

Hamiltonian Monte Carlo (HMC) exploits Hamiltonian dynamics to construct efficient proposals for Markov chain Monte Carlo (MCMC). In this paper, we present a generalization of HMC which exploits non-canonical Hamiltonian dynamics. We refer to this algorithm as magnetic HMC, since in 3 dimensions a subset of the dynamics map onto the mechanics of a charged particle coupled to a magnetic field. We establish a theoretical basis for the use of non-canonical Hamiltonian dynamics in MCMC, and construct a symplectic, leapfrog-like integrator allowing for the implementation of magnetic HMC. Finally, we exhibit several examples where these non-canonical dynamics can lead to improved mixing of magnetic HMC relative to ordinary HMC.

ICML Conference 2016 Conference Paper

Black-Box Alpha Divergence Minimization

José Miguel Hernández-Lobato
Yingzhen Li
Mark Rowland 0001
Thang D. Bui
Daniel Hernández-Lobato
Richard E. Turner

Black-box alpha (BB-α) is a new approximate inference method based on the minimization of α-divergences. BB-αscales to large datasets because it can be implemented using stochastic gradient descent. BB-αcan be applied to complex probabilistic models with little effort since it only requires as input the likelihood function and its gradients. These gradients can be easily obtained using automatic differentiation. By changing the divergence parameter α, the method is able to interpolate between variational Bayes (VB) (α→0) and an algorithm similar to expectation propagation (EP) (α= 1). Experiments on probit regression and neural network regression and classification problems show that BB-αwith non-standard settings of α, such as α= 0. 5, usually produces better predictions than with α→0 (VB) or α= 1 (EP).