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arXiv 2402.01371cs.LG
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函数逼近下平均奖励 MDP 的双时间尺度 Critic-Actor 算法

Two-Timescale Critic-Actor for Average Reward MDPs with Function Approximation

Indian Institute of Science(印度科学理工学院)

Prashansa Panda, Shalabh Bhatnagar

AI总结:

本文提出长期平均奖励 MDP 下首个带函数逼近的双时间尺度 critic-actor 算法,给出有限时间与渐近收敛保证,并在三个基准上验证其性能最优。

摘要:

近期若干工作聚焦于对 AC 算法进行非渐近收敛分析。最近,一种双时间尺度 critic-actor 算法被提出,用于查表情形下的折扣代价设定,其中 actor 与 critic 的时间尺度被反转,且仅证明了渐近收敛。在本工作中,我们提出了长期平均奖励设定下首个带函数逼近的双时间尺度 critic-actor 算法,并针对该方案给出首个有限时间非渐近收敛分析及渐近收敛分析。我们得到了最优学习率,并证明:为使 critic 的均方误差上界为 ε,本算法达到样本复杂度 $\mathcal{\tilde{O}}(ε^{-(2+δ)})$,其中 $δ>0$ 可任意接近零;这优于类似设定下双时间尺度 AC 所获得的结果。我们分析的一个显著特点是,除所得有限时间界外,还给出了该方案的渐近收敛分析,证明(较慢的)critic 递归几乎必然渐近收敛到一个相关微分包含的吸引子,此时 actor 参数对应于受扰平均奖励目标的局部极大值。我们还展示了在三个基准设定上的数值实验结果,并观察到我们的 critic-actor 算法在所有算法中表现最佳。

英文摘要:

Several recent works have focused on carrying out non-asymptotic convergence analyses for AC algorithms. Recently, a two-timescale critic-actor algorithm has been presented for the discounted cost setting in the look-up table case where the timescales of the actor and the critic are reversed and only asymptotic convergence shown. In our work, we present the first two-timescale critic-actor algorithm with function approximation in the long-run average reward setting and present the first finite-time non-asymptotic as well as asymptotic convergence analysis for such a scheme. We obtain optimal learning rates and prove that our algorithm achieves a sample complexity of {$\mathcal{\tilde{O}}(ε^{-(2+δ)})$ with $δ>0$ arbitrarily close to zero,} for the mean squared error of the critic to be upper bounded by $ε$ which is better than the one obtained for two-timescale AC in a similar setting. A notable feature of our analysis is that we present the asymptotic convergence analysis of our scheme in addition to the finite-time bounds that we obtain and show the almost sure asymptotic convergence of the (slower) critic recursion to the attractor of an associated differential inclusion with actor parameters corresponding to local maxima of a perturbed average reward objective. We also show the results of numerical experiments on three benchmark settings and observe that our critic-actor algorithm performs the best amongst all algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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