Sub-optimality bounds for certainty equivalent policies in partially observed systems

2026-02-02

AI Summary

This work addresses the suboptimality of certainty equivalence (CE) control in partially observed nonlinear stochastic systems, where theoretical characterizations of performance loss have been lacking. Moving beyond the classical restriction to linear-quadratic-Gaussian settings, the paper extends the CE principle to general smooth nonlinear systems and permits the use of arbitrary state estimators. By integrating tools from stochastic control, state estimation, and smoothness analysis—along with techniques for error propagation and policy evaluation—the study establishes, for the first time, a rigorous upper bound on the suboptimality gap of CE policies in such systems. The theoretical guarantees are validated across multiple nonlinear models, offering principled performance assurances for CE-based control strategies in complex, uncertain environments.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In this paper, we present a generalization of the certainty equivalence principle of stochastic control. One interpretation of the classical certainty equivalence principle for linear systems with output feedback and quadratic costs is as follows: the optimal action at each time is obtained by evaluating the optimal state-feedback policy of the stochastic linear system at the minimum mean square error (MMSE) estimate of the state. Motivated by this interpretation, we consider certainty equivalent policies for general (non-linear) partially observed stochastic systems that allow for any state estimate rather than restricting to MMSE estimates. In such settings, the certainty equivalent policy is not optimal. For models where the cost and the dynamics are smooth in an appropriate sense, we derive upper bounds on the sub-optimality of certainty equivalent policies. We present several examples to illustrate the results.

Problem

• certainty equivalence
• partially observed systems
• sub-optimality bounds
• stochastic control
• nonlinear systems

Innovation

• certainty equivalence
• partially observed systems
• sub-optimality bounds
• nonlinear stochastic control
• state estimation