Robust Control under Stationary Ambiguity

Control policies optimized in simulation can perform poorly in the real system when the parameters $x$ of the simulator are estimated from limited data but the resulting parameter uncertainty is not represented inside the simulation. A common way to incorporate such ambiguity is to simulate each trajectory of the system under a randomly drawn value for $x$. Since the policy cannot observe the drawn value, it must initially choose controls that perform well across many possible parameter values. However, if the policy progressively observes the system, it can often gradually infer the value of $x$, so that ambiguity vanishes. Over time, the policy then specializes to its estimate of $x$ and loses its robustness. This is undesirable in many real systems, where latent factors are expected to shift. In financial markets, for example, a policy hedging a derivative payoff should remain robust to changes in the volatility regime. To induce such continual robustness, we propose training policies in simulators where ambiguity varies with the system's state but does not systematically decay over time. We formalize this requirement as stationary ambiguity: the simulator should induce a stationary filter process over the latent state. We show how to construct such simulators and demonstrate, on hedging problems, that policies trained under stationary ambiguity preserve robustness to latent factors over time, leading to strong performance on real market data. As a modeling principle, stationary ambiguity informs many simulator design decisions: which models make realistic simulators, how their parameters should be randomized, and how simulator and policy should be initialized. While our experiments focus on hedging, stationary ambiguity may also be useful for other sequential control problems driven by exogenous stochastic processes with shifting latent structure.

HypEMBER: Hypernetwork-based Ensemble for Robust Policy Learning of Parametrized Dynamical Systems

In this work we investigate reinforcement learning (RL) as a framework for the robust control of parametrized dynamical systems in presence of measurements and model uncertainties. High-dimensional state spaces, expensive numerical solvers, the partial knowledge of the governing equations, and the dependence on physical parameters that may be uncertain or difficult to estimate accurately, make the use of standard RL approaches computationally unfeasible. Indeed, lack of robustness and poor generalization across parameter variations are further amplified in presence of noisy or incomplete measurements, ultimately hampering control performance. To address these challenges, we introduce HypEMBER, a novel RL framework based on the combination of hypernetworks and ensemble learning. In the proposed approach, both the policy and value functions are represented through hypernetworks that generate the weights of the underlying models conditioned on the physical parameters of the system, thereby enabling parametric generalization across different dynamical regimes. In addition, an ensemble of policy and value approximators is employed to quantify epistemic uncertainty, leading to improved exploration strategies and enhanced robustness during and after training. The performance of the proposed framework is assessed on two representative parametrized control problems: (i) the one-dimensional Kuramoto-Sivashinsky equation and (ii) a particle-navigation task in a two-dimensional time-dependent gyre flow, focusing on robustness with respect to measurement noise and parameter misspecification. Numerical results demonstrate that HypEMBER consistently improves training stability and sample efficiency, while achieving superior robustness to uncertainties affecting both the system dynamics and the available observations, in comparison with state-of-the-art RL methods.