Model-Free Linear Quadratic Control via Reduction to Expert Prediction
This work addresses the challenge of providing theoretical guarantees for model-free reinforcement learning in continuous control, offering a novel algorithm that achieves sublinear regret for linear quadratic systems, though it is incremental compared to model-based approaches.
The authors tackled the problem of model-free control in linear quadratic systems by reducing it to an expert prediction problem, achieving a regret bound of O(T^{ξ+2/3}) for any small ξ>0 with polynomial computation cost, which is the first such provable result in this setting.
Model-free approaches for reinforcement learning (RL) and continuous control find policies based only on past states and rewards, without fitting a model of the system dynamics. They are appealing as they are general purpose and easy to implement; however, they also come with fewer theoretical guarantees than model-based RL. In this work, we present a new model-free algorithm for controlling linear quadratic (LQ) systems, and show that its regret scales as $O(T^{ξ+2/3})$ for any small $ξ>0$ if time horizon satisfies $T>C^{1/ξ}$ for a constant $C$. The algorithm is based on a reduction of control of Markov decision processes to an expert prediction problem. In practice, it corresponds to a variant of policy iteration with forced exploration, where the policy in each phase is greedy with respect to the average of all previous value functions. This is the first model-free algorithm for adaptive control of LQ systems that provably achieves sublinear regret and has a polynomial computation cost. Empirically, our algorithm dramatically outperforms standard policy iteration, but performs worse than a model-based approach.