Policy Search: Any Local Optimum Enjoys a Global Performance Guarantee

Local Policy Search is a popular reinforcement learning approach for handling large state spaces. Formally, it searches locally in a paramet erized policy space in order to maximize the associated value function averaged over some predefined distribution. It is probably commonly b elieved that the best one can hope in general from such an approach is to get a local optimum of this criterion. In this article, we show th e following surprising result: \emph{any} (approximate) \emph{local optimum} enjoys a \emph{global performance guarantee}. We compare this g uarantee with the one that is satisfied by Direct Policy Iteration, an approximate dynamic programming algorithm that does some form of Poli cy Search: if the approximation error of Local Policy Search may generally be bigger (because local search requires to consider a space of s tochastic policies), we argue that the concentrability coefficient that appears in the performance bound is much nicer. Finally, we discuss several practical and theoretical consequences of our analysis

Soft-max boosting

International audienceThe standard multi-class classification risk, based on the binary loss, is rarely directly minimized. This is due to (i) the lack of convexity and (ii) the lack of smoothness (and even continuity). The classic approach consists in minimizing instead a convex surrogate. In this paper, we propose to replace the usually considered deterministic decision rule by a stochastic one, which allows obtaining a smooth risk (generalizing the expected binary loss, and more generally the cost-sensitive loss). Practically, this (empirical) risk is minimized by performing a gradient descent in the function space linearly spanned by a base learner (a.k.a. boosting). We provide a convergence analysis of the resulting algorithm and experiment it on a bunch of synthetic and real-world data sets (with noiseless and noisy domains, compared to convex and non-convex boosters)

A Theory of Regularized Markov Decision Processes

Many recent successful (deep) reinforcement learning algorithms make use of regularization, generally based on entropy or Kullback-Leibler divergence. We propose a general theory of regularized Markov Decision Processes that generalizes these approaches in two directions: we consider a larger class of regularizers, and we consider the general modified policy iteration approach, encompassing both policy iteration and value iteration. The core building blocks of this theory are a notion of regularized Bellman operator and the Legendre-Fenchel transform, a classical tool of convex optimization. This approach allows for error propagation analyses of general algorithmic schemes of which (possibly variants of) classical algorithms such as Trust Region Policy Optimization, Soft Q-learning, Stochastic Actor Critic or Dynamic Policy Programming are special cases. This also draws connections to proximal convex optimization, especially to Mirror Descent.Comment: ICML 201

Is the Bellman residual a bad proxy?

This paper aims at theoretically and empirically comparing two standard optimization criteria for Reinforcement Learning: i) maximization of the mean value and ii) minimization of the Bellman residual. For that purpose, we place ourselves in the framework of policy search algorithms, that are usually designed to maximize the mean value, and derive a method that minimizes the residual $\|T_* v_\pi - v_\pi\|_{1,\nu}$ over policies. A theoretical analysis shows how good this proxy is to policy optimization, and notably that it is better than its value-based counterpart. We also propose experiments on randomly generated generic Markov decision processes, specifically designed for studying the influence of the involved concentrability coefficient. They show that the Bellman residual is generally a bad proxy to policy optimization and that directly maximizing the mean value is much better, despite the current lack of deep theoretical analysis. This might seem obvious, as directly addressing the problem of interest is usually better, but given the prevalence of (projected) Bellman residual minimization in value-based reinforcement learning, we believe that this question is worth to be considered.Comment: Final NIPS 2017 version (title, among other things, changed

Difference of Convex Functions Programming Applied to Control with Expert Data

This paper reports applications of Difference of Convex functions (DC) programming to Learning from Demonstrations (LfD) and Reinforcement Learning (RL) with expert data. This is made possible because the norm of the Optimal Bellman Residual (OBR), which is at the heart of many RL and LfD algorithms, is DC. Improvement in performance is demonstrated on two specific algorithms, namely Reward-regularized Classification for Apprenticeship Learning (RCAL) and Reinforcement Learning with Expert Demonstrations (RLED), through experiments on generic Markov Decision Processes (MDP), called Garnets

CopyCAT: Taking Control of Neural Policies with Constant Attacks

We propose a new perspective on adversarial attacks against deep reinforcement learning agents. Our main contribution is CopyCAT, a targeted attack able to consistently lure an agent into following an outsider's policy. It is pre-computed, therefore fast inferred, and could thus be usable in a real-time scenario. We show its effectiveness on Atari 2600 games in the novel read-only setting. In this setting, the adversary cannot directly modify the agent's state -- its representation of the environment -- but can only attack the agent's observation -- its perception of the environment. Directly modifying the agent's state would require a write-access to the agent's inner workings and we argue that this assumption is too strong in realistic settings.Comment: AAMAS 202

A Dantzig Selector Approach to Temporal Difference Learning

LSTD is a popular algorithm for value function approximation. Whenever the number of features is larger than the number of samples, it must be paired with some form of regularization. In particular, L1-regularization methods tend to perform feature selection by promoting sparsity, and thus, are well-suited for high-dimensional problems. However, since LSTD is not a simple regression algorithm, but it solves a fixed--point problem, its integration with L1-regularization is not straightforward and might come with some drawbacks (e.g., the P-matrix assumption for LASSO-TD). In this paper, we introduce a novel algorithm obtained by integrating LSTD with the Dantzig Selector. We investigate the performance of the proposed algorithm and its relationship with the existing regularized approaches, and show how it addresses some of their drawbacks.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Optimisation de contrôleurs par essaim particulaire

http://cap2012.loria.fr/pub/Papers/10.pdfNational audienceTrouver des contrôleurs optimaux pour des systèmes stochastiques est un problème particulièrement difficile abordé dans les communautés d'apprentissage par renforcement et de contrôle optimal. Le paradigme classique employé pour résoudre ces problèmes est celui des processus décisionnel de Markov. Néanmoins, le problème d'optimisation qui en découle peut être difficile à résoudre. Dans ce papier, nous explorons l'utilisation de l'optimisation par essaim particulaire pour apprendre des contrôleurs optimaux. Nous l'appliquons en particulier à trois problèmes classiques : le pendule inversé, le mountain car et le double pendule

Off-policy Learning with Eligibility Traces: A Survey

In the framework of Markov Decision Processes, off-policy learning, that is the problem of learning a linear approximation of the value function of some fixed policy from one trajectory possibly generated by some other policy. We briefly review on-policy learning algorithms of the literature (gradient-based and least-squares-based), adopting a unified algorithmic view. Then, we highlight a systematic approach for adapting them to off-policy learning with eligibility traces. This leads to some known algorithms - off-policy LSTD(\lambda), LSPE(\lambda), TD(\lambda), TDC/GQ(\lambda) - and suggests new extensions - off-policy FPKF(\lambda), BRM(\lambda), gBRM(\lambda), GTD2(\lambda). We describe a comprehensive algorithmic derivation of all algorithms in a recursive and memory-efficent form, discuss their known convergence properties and illustrate their relative empirical behavior on Garnet problems. Our experiments suggest that the most standard algorithms on and off-policy LSTD(\lambda)/LSPE(\lambda) - and TD(\lambda) if the feature space dimension is too large for a least-squares approach - perform the best