Policy Gradient for LQR with Domain Randomization

-- Domain randomization (DR) enables sim-to-real transfer by training controllers on a distribution of simulated environments, with the goal of achieving robust performance in the real world. Although DR is widely used in practice and is often solved using simple policy gradient (PG) methods, understanding of its theoretical guarantees remains limited. T oward addressing this gap, we provide the first convergence analysis of PG methods for domain-randomized linear quadratic regulation (LQR). We show that PG converges globally to the minimizer of a finite-sample approximation of the DR objective under suitable bounds on the heterogeneity of the sampled systems. We also quantify the sample-complexity associated with achieving a small performance gap between the sample-average and population-level objectives. Additionally, we propose and analyze a discount-factor annealing algorithm that obviates the need for an initial jointly stabilizing controller, which may be challenging to find. Empirical results support our theoretical findings and highlight promising directions for future work, including risk-sensitive DR formulations and stochastic PG algorithms. Domain randomization (DR) has emerged as a dominant paradigm to enable transfer of policies optimized in simulation to the real world by randomizing simulator parameters during training [1-3]. In doing so, just as with robust control, DR accounts for discrepancies between the model used in simulation to synthesize a policy and the system that it is deployed on. Since DR does not solely focus on optimizing the worst-case performance, it can result in less conservative controller performance while still ensuring robust stability with high probability. Furthermore, DR can be easily implemented via first order methods. This makes it straightforward to incorporate into a wide variety of reinforcement learning schemes and to benefit from the increasing availability of parallel computation. Despite the ease with which DR can be implemented using first order methods, ensuring convergence of these methods remains a critical challenge, with practitioners relying upon complex scheduling of various hyperparameters in the optimization procedure [3].