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This research introduces a nonparametric variance-penalized actor-critic framework that eliminates the need for auxiliary networks by leveraging statistical bootstrapping and random scaling techniques. Theoretically grounded in stochastic approximation and ODE methods, the approach achieves bounded variance penalties with clean convergence analysis while matching or exceeding dual-critic baselines in standard environments. Its practical impact is demonstrated through a high-temperature superconductor manufacturing case study, where it significantly reduced yield variability, highlighting its utility for risk-sensitive optimization in complex physical systems.
Nonparametric Variance-Penalized Actor-Critic: Statistical Inference for Risk-Sensitive Reinforcement Learning
arXiv:2609.14327v1 Announce Type: new Abstract: Variance penalization is a principled approach to risk-sensitive reinforcement learning (RL) that explicitly trades expected return for policy stability. Existing methods require a dedicated second critic to estimate return variance online, adding architectural complexity and compounding estimation error during learning. We propose a nonparametric variance-penalized actor-critic (VPAC) framework that replaces the variance critic with statistically grounded online estimators based on bootstrapping and random scaling, techniques drawn from the statistical inference literature for stochastic approximation. These estimators require no auxiliary network, maintain a single-critic architecture, and produce variance penalties that are bounded by construction, enabling clean convergence analysis. We establish almost-sure convergence for both a variance-penalized Q-learning algorithm and a two-timescale actor-critic variant via the ordinary differential equation (ODE) method, requiring only that variance estimates remain bounded rather than consistent. Empirically, we evaluate across discrete and continuous stochastic environments, demonstrating that the proposed methods match or exceed the variance reduction achieved by the existing dual-critic VPAC baseline while eliminating the overhead of a second critic. We further validate on a high-temperature superconductor (HTS) manufacturing case study, where VPAC-RS (Random Scaling) achieves a 74% reduction in steady-state critical current variability and a 63% reduction in episode return standard deviation, translating directly to improved yield consistency. Our results establish nonparametric statistical inference as a practical and theoretically sound alternative to auxiliary critics for risk-sensitive RL.
Abstract:Variance penalization is a principled approach to risk-sensitive reinforcement learning (RL) that explicitly trades expected return for policy stability. Existing methods require a dedicated second critic to estimate return variance online, adding architectural complexity and compounding estimation error during learning. We propose a nonparametric variance-penalized actor-critic (VPAC) framework that replaces the variance critic with statistically grounded online estimators based on bootstrapping and random scaling, techniques drawn from the statistical inference literature for stochastic approximation. These estimators require no auxiliary network, maintain a single-critic architecture, and produce variance penalties that are bounded by construction, enabling clean convergence analysis. We establish almost-sure convergence for both a variance-penalized Q-learning algorithm and a two-timescale actor-critic variant via the ordinary differential equation (ODE) method, requiring only that variance estimates remain bounded rather than consistent. Empirically, we evaluate across discrete and continuous stochastic environments, demonstrating that the proposed methods match or exceed the variance reduction achieved by the existing dual-critic VPAC baseline while eliminating the overhead of a second critic. We further validate on a high-temperature superconductor (HTS) manufacturing case study, where VPAC-RS (Random Scaling) achieves a 74% reduction in steady-state critical current variability and a 63% reduction in episode return standard deviation, translating directly to improved yield consistency. Our results establish nonparametric statistical inference as a practical and theoretically sound alternative to auxiliary critics for risk-sensitive RL.
Submitted to IEEE Transactions on Neural Networks and Learning Systems. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2609.14327 [cs.LG]
(or arXiv:2609.14327v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.14327 arXiv-issued DOI via DataCite (pending registration)
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