The Best of Both Worlds: Reinforcement Learning with Logarithmic Regret and Policy Switches

by   Grigoris Velegkas, et al.

In this paper, we study the problem of regret minimization for episodic Reinforcement Learning (RL) both in the model-free and the model-based setting. We focus on learning with general function classes and general model classes, and we derive results that scale with the eluder dimension of these classes. In contrast to the existing body of work that mainly establishes instance-independent regret guarantees, we focus on the instance-dependent setting and show that the regret scales logarithmically with the horizon T, provided that there is a gap between the best and the second best action in every state. In addition, we show that such a logarithmic regret bound is realizable by algorithms with O(log T) switching cost (also known as adaptivity complexity). In other words, these algorithms rarely switch their policy during the course of their execution. Finally, we complement our results with lower bounds which show that even in the tabular setting, we cannot hope for regret guarantees lower than o(log T).



page 1

page 2

page 3

page 4


Logarithmic Regret for Reinforcement Learning with Linear Function Approximation

Reinforcement learning (RL) with linear function approximation has recei...

Almost Optimal Model-Free Reinforcement Learning via Reference-Advantage Decomposition

We study the reinforcement learning problem in the setting of finite-hor...

Regret Bounds for Reinforcement Learning with Policy Advice

In some reinforcement learning problems an agent may be provided with a ...

Gap-Dependent Bounds for Two-Player Markov Games

As one of the most popular methods in the field of reinforcement learnin...

Exponential Bellman Equation and Improved Regret Bounds for Risk-Sensitive Reinforcement Learning

We study risk-sensitive reinforcement learning (RL) based on the entropi...

Universal Algorithms: Beyond the Simplex

The bulk of universal algorithms in the online convex optimisation liter...

Provably adaptive reinforcement learning in metric spaces

We study reinforcement learning in continuous state and action spaces en...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.