Heng Yang

Zhiyu Zhang, David Bombara, Heng Yang · harvard

We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the discounted regret in online convex optimization, and propose an adaptive (i.e., instance optimal), FTRL-based algorithm that improves the widespread non-adaptive baseline -- gradient descent with a constant learning rate. From a practical perspective, this refines the classical idea of regularization in lifelong learning: we show that designing good regularizers can be guided by the principled theory of adaptive online optimization. Complementing this result, we also consider the (Gibbs and Candès, 2021)-style online conformal prediction problem, where the goal is to sequentially predict the uncertainty sets of a black-box machine learning model. We show that the FTRL nature of our algorithm can simplify the conventional gradient-descent-based analysis, leading to instance-dependent performance guarantees.

Haoyu Han, Heng Yang

Policy-gradient methods are widely used in reinforcement learning, yet training often becomes unstable or slows down as learning progresses. We study this phenomenon through the noise-to-signal ratio (NSR) of a policy-gradient estimator, defined as the estimator variance (noise) normalized by the squared norm of the true gradient (signal). Our main result is that, for (i) finite-horizon linear systems with Gaussian policies and linear state-feedback, and (ii) finite-horizon polynomial systems with Gaussian policies and polynomial feedback, the NSR of the REINFORCE estimator can be characterized exactly-either in closed form or via numerical moment-evaluation algorithms-without approximation. For general nonlinear dynamics and expressive policies (including neural policies), we further derive a general upper bound on the variance. These characterizations enable a direct examination of how NSR varies across policy parameters and how it evolves along optimization trajectories (e.g. SGD and Adam). Across a range of examples, we find that the NSR landscape is highly non-uniform and typically increases as the policy approaches an optimum; in some regimes it blows up, which can trigger training instability and policy collapse.

Runhan Huang, Haldun Balim, Heng Yang et al.

Legged locomotion demands controllers that are both robust and adaptable, while remaining compatible with task and safety considerations. However, model-free reinforcement learning (RL) methods often yield a fixed policy that can be difficult to adapt to new behaviors at test time. In contrast, Model Predictive Control (MPC) provides a natural approach to flexible behavior synthesis by incorporating different objectives and constraints directly into its optimization process. However, classical MPC relies on accurate dynamics models, which are often difficult to obtain in complex environments and typically require simplifying assumptions. We present Diffusion-MPC, which leverages a learned generative diffusion model as an approximate dynamics prior for planning, enabling flexible test-time adaptation through reward and constraint based optimization. Diffusion-MPC jointly predicts future states and actions; at each reverse step, we incorporate reward planning and impose constraint projection, yielding trajectories that satisfy task objectives while remaining within physical limits. To obtain a planning model that adapts beyond imitation pretraining, we introduce an interactive training algorithm for diffusion based planner: we execute our reward-and-constraint planner in environment, then filter and reweight the collected trajectories by their realized returns before updating the denoiser. Our design enables strong test-time adaptability, allowing the planner to adjust to new reward specifications without retraining. We validate Diffusion-MPC on real world, demonstrating strong locomotion and flexible adaptation.