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Abstract

This paper considers the problem of adapting a predesigned policy, represented by a parameterized function class, from a solution that minimizes a given original cost function to a trade-off solution between minimizing the original objective and an additional cost function. The problem is formulated as a constrained optimization problem, where deviations from the optimal value of the original cost are explicitly constrained. To solve it, we develop a closed-loop system that governs the evolution of the policy parameters, with a closed-loop controller designed to adjust the additional cost gradient to ensure the satisfaction of the constraint. The resulting closed-loop system, termed control-barrier-function-based policy adaptation, exploits the set-invariance property of control barrier functions to guarantee constraint satisfaction. The effectiveness of the proposed method is demonstrated through numerical experiments on the Cartpole and Lunar Lander benchmarks from OpenAI Gym, as well as a quadruped robot, thereby illustrating both its practicality and potential for real-world policy adaptation.