提出无需调参的时序差分学习方法,让理论更贴近实际应用。
Towards Parameter-Free Temporal Difference Learning
- 用指数步长调度替代传统参数,避免依赖难估计的问题量。
- 在独立同分布和马尔可夫采样下均实现最优偏差-方差平衡。
- 无需投影、平均或先验知识,适合真实强化学习场景使用。
时序差分(TD)学习是强化学习中估计价值函数的核心算法。近期对线性函数逼近下TD的有限时间分析虽量化了收敛速率,但常需依赖难以估计的问题相关量,如特征协方差最小特征值(ω)或马尔可夫链混合时间(τ_mix)。部分分析还依赖非标准且不实用的修改,加剧了理论与实践的差距。为此,本文采用指数步长调度的TD(0)算法,在独立同分布采样与单轨迹马尔可夫采样两种情形下进行分析。在独立同分布设置中,该方法无需ω等量,即可实现最后迭代点的最优偏差-方差权衡。在马尔可夫设置中,提出带指数步长的正则化TD(0),达到与先前工作相当的收敛速率,且无需投影、迭代平均或τ_mix、ω等先验知识。
原文摘要 · Abstract (English)
Temporal difference (TD) learning is a fundamental algorithm for estimating value functions in reinforcement learning. Recent finite-time analyses of TD with linear function approximation quantify its theoretical convergence rate. However, they often require setting the algorithm parameters using problem-dependent quantities that are difficult to estimate in practice -- such as the minimum eigenvalue of the feature covariance (\(ω\)) or the mixing time of the underlying Markov chain (\(τ_{\text{mix}}\)). In addition, some analyses rely on nonstandard and impractical modifications, exacerbating the gap between theory and practice. To address these limitations, we use an exponential step-size schedule with the standard TD(0) algorithm. We analyze the resulting method under two sampling regimes: independent and identically distributed (i.i.d.) sampling from the stationary distribution, and the more practical Markovian sampling along a single trajectory. In the i.i.d.\ setting, the proposed algorithm does not require knowledge of problem-dependent quantities such as \(ω\), and attains the optimal bias-variance trade-off for the last iterate. In the Markovian setting, we propose a regularized TD(0) algorithm with an exponential step-size schedule. The resulting algorithm achieves a comparable convergence rate to prior works, without requiring projections, iterate averaging, or knowledge of \(τ_{\text{mix}}\) or \(ω\).
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。