Victor Gabillon

ICML Conference 2019 Conference Paper

Scale-free adaptive planning for deterministic dynamics & discounted rewards

• Peter L. Bartlett
• Victor Gabillon
• Jennifer Healey
• Michal Valko

We address the problem of planning in an environment with deterministic dynamics and stochastic discounted rewards under a limited numerical budget where the ranges of both rewards and noise are unknown. We introduce PlaTypOOS, an adaptive, robust, and efficient alternative to the OLOP (open-loop optimistic planning) algorithm. Whereas OLOP requires a priori knowledge of the ranges of both rewards and noise, PlaTypOOS dynamically adapts its behavior to both. This allows PlaTypOOS to be immune to two vulnerabilities of OLOP: failure when given underestimated ranges of noise and rewards and inefficiency when these are overestimated. PlaTypOOS additionally adapts to the global smoothness of the value function. PlaTypOOS acts in a provably more efficient manner vs. OLOP when OLOP is given an overestimated reward and show that in the case of no noise, PlaTypOOS learns exponentially faster.

NeurIPS Conference 2017 Conference Paper

Near Minimax Optimal Players for the Finite-Time 3-Expert Prediction Problem

• Yasin Abbasi Yadkori
• Peter Bartlett
• Victor Gabillon

We study minimax strategies for the online prediction problem with expert advice. It has been conjectured that a simple adversary strategy, called COMB, is near optimal in this game for any number of experts. Our results and new insights make progress in this direction by showing that, up to a small additive term, COMB is minimax optimal in the finite-time three expert problem. In addition, we provide for this setting a new near minimax optimal COMB-based learner. Prior to this work, in this problem, learners obtaining the optimal multiplicative constant in their regret rate were known only when $K=2$ or $K\rightarrow\infty$. We characterize, when $K=3$, the regret of the game scaling as $\sqrt{8/(9\pi)T}\pm \log(T)^2$ which gives for the first time the optimal constant in the leading ($\sqrt{T}$) term of the regret.

JMLR Journal 2015 Journal Article

Approximate Modified Policy Iteration and its Application to the Game of Tetris

• Bruno Scherrer
• Mohammad Ghavamzadeh
• Victor Gabillon
• Boris Lesner
• Matthieu Geist

Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three implementations of approximate MPI (AMPI) that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide error propagation analysis that unify those for approximate policy and value iteration. We develop the finite-sample analysis of these algorithms, which highlights the influence of their parameters. In the classification-based version of the algorithm (CBMPI), the analysis shows that MPI's main parameter controls the balance between the estimation error of the classifier and the overall value function approximation. We illustrate and evaluate the behavior of these new algorithms in the Mountain Car and Tetris problems. Remarkably, in Tetris, CBMPI outperforms the existing DP approaches by a large margin, and competes with the current state-of-the-art methods while using fewer samples. [abs] [ pdf ][ bib ] &copy JMLR 2015. ( edit, beta )

AAAI Conference 2014 Conference Paper

Large-Scale Optimistic Adaptive Submodularity

• Victor Gabillon
• Branislav Kveton
• Zheng Wen
• Brian Eriksson
• S. Muthukrishnan

Maximization of submodular functions has wide applications in artificial intelligence and machine learning. In this paper, we propose a scalable learning algorithm for maximizing an adaptive submodular function. The key structural assumption in our solution is that the state of each item is distributed according to a generalized linear model, which is conditioned on the feature vector of the item. Our objective is to learn the parameters of this model. We analyze the performance of our algorithm, and show that its regret is polylogarithmic in time and quadratic in the number of features. Finally, we evaluate our solution on two problems, preference elicitation and face detection, and show that high-quality policies can be learned sample efficiently.

NeurIPS Conference 2013 Conference Paper

Adaptive Submodular Maximization in Bandit Setting

• Victor Gabillon
• Branislav Kveton
• Zheng Wen
• Brian Eriksson
• S. Muthukrishnan

Maximization of submodular functions has wide applications in machine learning and artificial intelligence. Adaptive submodular maximization has been traditionally studied under the assumption that the model of the world, the expected gain of choosing an item given previously selected items and their states, is known. In this paper, we study the scenario where the expected gain is initially unknown and it is learned by interacting repeatedly with the optimized function. We propose an efficient algorithm for solving our problem and prove that its expected cumulative regret increases logarithmically with time. Our regret bound captures the inherent property of submodular maximization, earlier mistakes are more costly than later ones. We refer to our approach as Optimistic Adaptive Submodular Maximization (OASM) because it trades off exploration and exploitation based on the optimism in the face of uncertainty principle. We evaluate our method on a preference elicitation problem and show that non-trivial K-step policies can be learned from just a few hundred interactions with the problem.

NeurIPS Conference 2013 Conference Paper

Approximate Dynamic Programming Finally Performs Well in the Game of Tetris

• Victor Gabillon
• Mohammad Ghavamzadeh
• Bruno Scherrer

Tetris is a popular video game that has been widely used as a benchmark for various optimization techniques including approximate dynamic programming (ADP) algorithms. A close look at the literature of this game shows that while ADP algorithms, that have been (almost) entirely based on approximating the value function (value function based), have performed poorly in Tetris, the methods that search directly in the space of policies by learning the policy parameters using an optimization black box, such as the cross entropy (CE) method, have achieved the best reported results. This makes us conjecture that Tetris is a game in which good policies are easier to represent, and thus, learn than their corresponding value functions. So, in order to obtain a good performance with ADP, we should use ADP algorithms that search in a policy space, instead of the more traditional ones that search in a value function space. In this paper, we put our conjecture to test by applying such an ADP algorithm, called classification-based modified policy iteration (CBMPI), to the game of Tetris. Our extensive experimental results show that for the first time an ADP algorithm, namely CBMPI, obtains the best results reported in the literature for Tetris in both small $10\times 10$ and large $10\times 20$ boards. Although the CBMPI's results are similar to those achieved by the CE method in the large board, CBMPI uses considerably fewer (almost 1/10) samples (call to the generative model of the game) than CE.

ICML Conference 2012 Conference Paper

Approximate Modified Policy Iteration

• Bruno Scherrer
• Victor Gabillon
• Mohammad Ghavamzadeh
• Matthieu Geist

NeurIPS Conference 2012 Conference Paper

Best Arm Identification: A Unified Approach to Fixed Budget and Fixed Confidence

• Victor Gabillon
• Mohammad Ghavamzadeh
• Alessandro Lazaric

We study the problem of identifying the best arm(s) in the stochastic multi-armed bandit setting. This problem has been studied in the literature from two different perspectives: fixed budget and fixed confidence. We propose a unifying approach that leads to a meta-algorithm called unified gap-based exploration (UGapE), with a common structure and similar theoretical analysis for these two settings. We prove a performance bound for the two versions of the algorithm showing that the two problems are characterized by the same notion of complexity. We also show how the UGapE algorithm as well as its theoretical analysis can be extended to take into account the variance of the arms and to multiple bandits. Finally, we evaluate the performance of UGapE and compare it with a number of existing fixed budget and fixed confidence algorithms.

ICML Conference 2011 Conference Paper

Classification-based Policy Iteration with a Critic

• Victor Gabillon
• Alessandro Lazaric
• Mohammad Ghavamzadeh
• Bruno Scherrer

NeurIPS Conference 2011 Conference Paper

Multi-Bandit Best Arm Identification

• Victor Gabillon
• Mohammad Ghavamzadeh
• Alessandro Lazaric
• Sébastien Bubeck

We study the problem of identifying the best arm in each of the bandits in a multi-bandit multi-armed setting. We first propose an algorithm called Gap-based Exploration (GapE) that focuses on the arms whose mean is close to the mean of the best arm in the same bandit (i. e. , small gap). We then introduce an algorithm, called GapE-V, which takes into account the variance of the arms in addition to their gap. We prove an upper-bound on the probability of error for both algorithms. Since GapE and GapE-V need to tune an exploration parameter that depends on the complexity of the problem, which is often unknown in advance, we also introduce variations of these algorithms that estimate this complexity online. Finally, we evaluate the performance of these algorithms and compare them to other allocation strategies on a number of synthetic problems.