Adaptive Variants of Optimal Feedback Policies

TL;DR

This paper introduces a control-theoretic framework for adaptive optimal feedback policies that maintain effectiveness under parameter variations in uncertain nonlinear systems, with applications in transfer learning and sim-to-real transfer.

Contribution

It proposes a systematic method for adaptive control laws that ensure stability and near-optimal performance despite significant parametric uncertainties.

Findings

Guarantees convergence to zero cost state

Maintains effectiveness in transfer learning scenarios

Achieves near-optimal performance on mountain car problem

Abstract

The stable combination of optimal feedback policies with online learning is studied in a new control-theoretic framework for uncertain nonlinear systems. The framework can be systematically used in transfer learning and sim-to-real applications, where an optimal policy learned for a nominal system needs to remain effective in the presence of significant variations in parameters. Given unknown parameters within a bounded range, the resulting adaptive control laws guarantee convergence of the closed-loop system to the state of zero cost. Online adjustment of the learning rate is used as a key stability mechanism, and preserves certainty equivalence when designing optimal policies without assuming uncertainty to be within the control range. The approach is illustrated on the familiar mountain car problem, where it yields near-optimal performance despite the presence of parametric model uncertainty.