Authors: Konrad J. Mueller, Amira Akkari, Ben Wood, Lukas Gonon
Organizations: 1Imperial College London · 2JPMorgan Chase & Co.† · University of St. Gallen
Abstract
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.
Real-world control systems frequently operate under \emph{piecewise stationary} conditions, where dynamics remain stable for extended periods before undergoing abrupt regime changes. Standard robust RL methods face a fundamental dilemma: a globally conservative policy wastes performance during stable periods, while a locally adaptive policy risks catastrophic failure when the regime changes undetected. We propose \textbf{BAPR} (Bayesian Amnesic Piecewise-Robust SAC), which unifies Bayesian Online Change Detection (BOCD) with robust ensemble RL. The BAPR operator -- a convex combination of mode-conditional Bellman operators weighted by a frozen belief distribution -- is a γ-contraction. A complementary counterexample, machine-verified in Lean4, establishes a \emph{sharp boundary}: when beliefs depend on the Q-function, the contraction factor becomes γ+λΔ (where Δ is the mode reward gap), and contraction fails exactly when γ+λΔ≥1. We derive a \emph{component-wise} formal error budget for the abstract operator -- every component machine-verified -- bounding post-switch recovery; the budget applies to the abstract mode-mixture operator and inherits to the implemented shared-critic algorithm only through the frozen-parameter design intuition. All results are formally verified with no \texttt{sorry} (1,145 lines across 3 Lean4 files, 22 machine-verified theorems). BOCD drives an adaptive conservatism mechanism: the policy becomes maximally conservative after detected change-points and smoothly relaxes as confidence grows, with detection delay O(log(1/δ)). A context-conditioning module trained via RMDM loss provides mode-aware representations from simulator-provided mode IDs at training time and requires no mode labels at deployment.
In policy gradient reinforcement learning, access to a differentiable model enables 1st-order gradient estimation that accelerates learning compared to relying solely on derivative-free 0th-order estimators. However, discontinuous dynamics cause bias and undermine the effectiveness of 1st-order estimators. Prior work addressed this bias by constructing a confidence interval around the REINFORCE 0th-order gradient estimator and using these bounds to detect discontinuities. However, the REINFORCE estimator is notoriously noisy, and we find that this method requires task-specific hyperparameter tuning and has low sample efficiency. This paper asks whether such bias is the primary obstacle and what minimal fixes suffice. First, we re-examine standard discontinuous settings from prior work and introduce DDCG, a lightweight test that switches estimators in nonsmooth regions; with a single hyperparameter, DDCG achieves robust performance and remains reliable with small samples. Second, on differentiable robotics control tasks, we present IVW-H, a per-step inverse-variance implementation that stabilizes variance without explicit discontinuity detection and yields strong results. Together, these findings indicate that while estimator switching improves robustness in controlled studies, careful variance control often dominates in practical deployments.
Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of uncertainty from an explicit probability law to the sampler induced by the learned generator. Reliability therefore depends on two errors: sampler misspecification and finite-simulation error. We propose Sampler-Robust Optimization (SRO), which optimizes decisions against the worst-case sampler induced by perturbing the learned generator. This sampler-first formulation aligns with simulation-based decision pipelines and admits a sharpness-aware interpretation: it favors decisions whose performance is stable under generator perturbations, rather than merely under the nominal sampler. Under a coverage assumption, we show that the empirical worst-case objective provides a high-probability upper certificate for the true population objective, with finite-simulation error partially absorbed by the robustification used to guard against sampler misspecification. The framework accommodates generative models with or without explicit densities and admits efficient minimax procedures. Portfolio-optimization experiments show that SRO produces more stable decisions and improves out-of-sample performance under distribution shift.