提出更稳定的量化目标优化方法,提升强化学习在医疗金融等高风险场景的可靠性。
Risk-Sensitive Reinforcement Learning with Smoothed Quantile Objectives
- 用缓冲量化准则平滑原始分位数目标,增强对模型误差的鲁棒性
- 算法在有限步内实现近似最优,理论证明其累积损失增长速度可控
- 适用于对决策稳定性要求高的医疗、金融等风险敏感领域
强化学习虽取得显著进展,但传统方法未考虑目标函数的风险敏感性,而该特性在医疗、金融等领域至关重要。现有方法通过优化累积奖励分布的特定分位数来引入风险敏感性,但精确分位数目标非光滑且对回报分布微小扰动敏感,难以从数据中可靠学习。为此,本文提出基于乐观学习的模型化算法UCB-BQRL,维护转移核的置信集,并使用下缓冲分位数准则进行规划。该缓冲准则通过平均邻近低分位数平滑原始分位数目标,提升在转移估计误差下的稳定性。为每轮计算缓冲分位数策略,引入精确动态规划方法EVI-BQ。理论证明:UCB-BQRL在高概率下具有 cal{O}(\mathrm{e}^{τ/ρ_τ}+H^2\sqrt{SAT})的后悔上界,其中ρ_τ为问题相关常数(根层左平台阈值)。进一步建立信息论下界Ω(H/ρ_τ\sqrt{AT}),表明任何处理分位数目标的算法均无法更优。最后,证明精确点分位数评估与下缓冲分位数评估在多项式时间图灵归约下均为PP-hard,即使在两状态、单动作的有限时域马尔可夫决策过程固定策略下也如此。
原文摘要 · Abstract (English)
Reinforcement Learning (RL) has achieved tremendous success in recent years. However, the classical foundations of RL do not account for the risk sensitivity of the objective function, which is critical in various fields, including healthcare, finance, etc. A popular approach to incorporate risk sensitivity is to optimize a specific quantile of the cumulative reward distribution. However, exact quantile objectives are non-smooth and can change abruptly under small perturbations of the return distribution, making them difficult to optimize reliably when the transition model must be learned from data. Motivated by this instability, we develop UCB-BQRL, a model-based optimistic learning algorithm that maintains confidence sets for the transition kernel and plans using a lower-buffered quantile criterion. The buffered criterion smooths the exact quantile objective by averaging nearby lower quantiles, thereby improving stability under transition-estimation error. To compute the buffered-quantile policy at each episode, we introduce EVI-BQ, an exact dynamic-programming procedure. We establish a high-probability regret bound for UCB-BQRL, which up to logarithmic factors scales as $\mathcal{O}(\mathrm{e}^{τ/ρ_τ}+H^2\sqrt{SAT})$, where $ρ_τ$ is denoted as the root-level left-plateau threshold, which is a problem-dependent constant. Further, we establish an information-theoretic lower bound of $Ω(H/ρ_τ\sqrt{AT})$ for the regret of any algorithm dealing with a quantile objective function. Finally, we prove that the exact point-quantile evaluation and exact lower-buffered quantile evaluation are PP-hard under polynomial-time Turing reductions, even for a fixed policy in a two-state, one-action finite-horizon MDP.
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