We consider the problem of objective inference in the context of receding-horizon linear-quadratic regulator (LQR). In this setting, we are given sequential state-action observations, where each observed action is the first control of a newly solved finite-horizon LQR problem. We characterize when the objective of that problem is uniquely identifiable from these observations and when additional observations provide no new information about the objective. We then analyze action prediction at unseen states and show that all objectives reproducing the observed actions yield identical actions throughout the affine hull of the observed states; outside this hull, we derive an upper bound on the prediction error. % and deriving a prediction-error bound outside this hull. Additionally, we show that, when only the linear objective terms are unknown, exact prediction holds at every state. Finally, numerical results show that, even under stochastic observation noise, re-optimizing an inferred objective enables accurate action prediction at unseen states across different planning horizons.
Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this challenge for stochastic controlled nonlinear dynamical systems whose state is observed along a single trajectory. Our goal is to reconstruct the unknown controlled state-incre...
Juncal Arbelaiz, Anushri Arora, Jonathan W. Pillow· 0 citations
A new framework for flexible, nonlinear, and interpretable off-policy evaluation for infinite-horizon reinforcement learning is developed and a group-sparsity-based feature screening procedure is proposed that identifies, with high probability, a reduced feature set containing all relevant covariates.
Recursive state estimation often executes approximate numerical solutions inside a feedback loop, where highly accurate local steps do not guarantee better overall results. For a fixed linear Kalman model, we characterize when a correction within a prescribed subspace and norm budget can meet a local admissibility tole...
Yanjun Ji, D. Willsch, Orkun Şensebat et al.· 0 citations
The Frank--Wolfe framework is extended to input design for system identification with unknown dynamics and adaptive online LQR, and an $\mathcal{O}(1/M)$ convergence rate is established for the objective value, while strong convexity yields an $\mathcal{O}(1/\sqrt{M})$ rate for the iterates.
Fethi Bencherki, Bruce D. Lee, Nikolai Matni et al.· 0 citations
It is shown that, even for the covariance steering problem with a broad class of commonly used state and control safety constraints, the synthesized Markovian policy almost surely produces the same control actions as the history-dependent policy and therefore the same state trajectories, cost, and moments.
Inverse game theory seeks to learn agents'unknown objectives from observed equilibrium behavior. Existing residual-based approaches can lead to non-convex problems and need not ensure strong monotonicity of the learned game, limiting reliable equilibrium prediction. We develop a tractable convex framework for learning...
Arghya Mallick, R. R. Baghbadorani, Peyman Mohajerin Esfahani et al.· 0 citations
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