End-to-end QP-based policies: A unified perspective on robust control and robot learning

A key challenge towards reliable robotic control is devising computational models that can both learn policies and guarantee robustness when deployed in the field. Inspired by the free energy principle in computational neuroscience, to address these challenges, we propose a model for policy computation that jointly learns environment dynamics and rewards, while ensuring robustness to epistemic uncertainties. Expounding a distributionally robust free energy principle, we propose a modification to the maximum diffusion learning framework. After explicitly characterizing robustness of our policies to epistemic uncertainties in both environment and reward, we validate their effectiveness on continuous-control benchmarks, via both simulations and real-world experiments involving manipulation with a Franka Research~3 arm. Across simulation and zero-shot deployment, our approach narrows the sim-to-real gap, and enables repeatable tabletop manipulation without task-specific fine-tuning.

Distributionally robust reinforcement learning seeks policies that remain effective when the deployment environment differs from the one that generated the training data. We study model-free robust Q-learning with $χ^2$ uncertainty sets and linear function approximation, using data from a single trajectory of an unknown nominal MDP. Evaluating the $χ^2$ robust Bellman target introduces the square root of a conditional second moment, which cannot be estimated unbiasedly from one transition, while the projected robust Bellman operator need not be contractive. We address these obstacles through a variational reformulation of the robust Bellman target and a blockwise frozen-target scheme, and establish a finite-time error bound relative to the optimal robust Q-function for every $γ\in(0,1)$. A neural-network experiment illustrates how the variational target can be used in a continuous-state nonlinear-control task.

Robots deployed in the real world rarely operate under a single fixed dynamics model: wind changes, payloads vary, batteries drain, contacts shift, and hardware wears. Yet most learning-based controllers are trained once and deployed as if learning were complete. This prevents the robot from using deployment experience to further improve task performance. In this work, we propose a continual learning framework that uses real-world experience to improve robot policies under hidden and recurring dynamics. Our method learns a condition-aware dynamics model from real state-action trajectories by combining an analytical physics prior with a neural residual for unmodeled effects. A recurrent encoder infers the current hidden condition from recent interaction, and this estimate conditions both the residual model and the policy. Policy learning is performed via differentiable simulation using diverse learned dynamics sampled from the latent model. At deployment, these sampled conditions are replaced by conditions inferred online from recent real interaction, allowing the policy to recover recurring dynamics by recognition rather than residual re-fitting. Through extensive simulation studies and real-world experiments, we demonstrate that the framework improves policy performance under diverse unobserved disturbances. On real quadrotor trajectory tracking under changing wind, the policy recovers from recurring disturbances in roughly 1s, about 5x faster than online residual re-fitting. It also reduces large-disturbance hover and tracking errors by 65.7% and 53.3% over the state-of-the-art online adaptation approaches