A Nearly Optimal and Low-Switching Algorithm for Reinforcement Learning with General Function Approximation

TL;DR

This paper introduces MQL-UCB, a reinforcement learning algorithm that achieves near-optimal regret and low policy switching costs using a novel deterministic switching strategy, monotonic value functions, and variance-weighted regression.

Contribution

The paper presents a new RL algorithm with a deterministic policy-switching strategy, monotonic value functions, and variance-weighted regression, achieving minimax optimal regret and low switching costs.

Findings

Achieves minimax optimal regret of  O(d\u221A HK)

Near-optimal policy switching cost of  O(dH)

Effective for general function approximation with provable guarantees

Abstract

The exploration-exploitation dilemma has been a central challenge in reinforcement learning (RL) with complex model classes. In this paper, we propose a new algorithm, Monotonic Q-Learning with Upper Confidence Bound (MQL-UCB) for RL with general function approximation. Our key algorithmic design includes (1) a general deterministic policy-switching strategy that achieves low switching cost, (2) a monotonic value function structure with carefully controlled function class complexity, and (3) a variance-weighted regression scheme that exploits historical trajectories with high data efficiency. MQL-UCB achieves minimax optimal regret of $\tilde{O}(d\sqrt{HK})$ when $K$ is sufficiently large and near-optimal policy switching cost of $\tilde{O}(dH)$, with $d$ being the eluder dimension of the function class, $H$ being the planning horizon, and $K$ being the number of episodes. Our work sheds light on designing provably sample-efficient and deployment-efficient Q-learning with nonlinear function approximation.