Quasi-Stochastic Approximation and Off-Policy Reinforcement Learning

The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning (RL), and often an efficient approach to solving (or approximating the solution to) complex optimal control problems. However, in many cases practitioners are unable to appl...

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Bibliographic Details
Published in:Proceedings of the IEEE Conference on Decision & Control pp. 5244 - 5251
Main Authors: Bernstein, Andrey, Chen, Yue, Colombino, Marcello, Dall'Anese, Emiliano, Mehta, Prashant, Meyn, Sean
Format: Conference Proceeding
Language:English
Published: IEEE 01.12.2019
Subjects:
Approximation algorithms
Convergence
Government
Monte Carlo methods
Optimization
Perturbation methods
Stochastic processes
ISSN:2576-2370
Online Access:Get full text
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Summary:The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning (RL), and often an efficient approach to solving (or approximating the solution to) complex optimal control problems. However, in many cases practitioners are unable to apply these techniques because of an inherent high variance. This paper aims to provide a general foundation for "quasistochastic approximation," in which all of the processes under consideration are deterministic, much like quasi-Monte-Carlo for variance reduction in simulation. The variance reduction can be substantial, subject to tuning of pertinent parameters in the algorithm. This paper introduces a new coupling argument to establish optimal rate of convergence provided the gain is sufficiently large. These results are established for linear models, and tested also in non-ideal settings. A major application of these general results is a new class of RL algorithms for deterministic state space models. In this setting, the main contribution is a class of algorithms for approximating the value function for a given policy, using a different policy designed to introduce exploration.
ISSN:2576-2370
DOI:10.1109/CDC40024.2019.9029247