決定論的ダイナミクスにおける線形ベルマン完全性下での計算効率の良い強化学習
Computationally Efficient RL under Linear Bellman Completeness for Deterministic Dynamics
線形ベルマン完全性を満たす決定論的MDPに対し、最小二乗回帰にランダムノイズを注入する楽観的価値反復により、計算効率の良い強化学習アルゴリズムを提案した。
著者: Runzhe Wu, Ayush Sekhari, Akshay Krishnamurthy, Wen Sun
分類: cs.LG, cs.RO, cs.SY, eess.SY
原文アブストラクト
We study computationally and statistically efficient Reinforcement Learning algorithms for the linear Bellman Complete setting. This setting uses linear function approximation to capture value functions and unifies existing models like linear Markov Decision Processes (MDP) and Linear Quadratic Regulators (LQR). While it is known from the prior works that this setting is statistically tractable, it remained open whether a computationally efficient algorithm exists. Our work provides a computationally efficient algorithm for the linear Bellman complete setting that works for MDPs with large action spaces, random initial states, and random rewards but relies on the underlying dynamics to be deterministic. Our approach is based on randomization: we inject random noise into least squares regression problems to perform optimistic value iteration. Our key technical contribution is to carefully design the noise to only act in the null space of the training data to ensure optimism while circumventing a subtle error amplification issue.
