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# SEAGuL: Sample Efficient Adversarially Guided Learning of Value Functions

*Proceedings of the 3rd Conference on Learning for Dynamics and Control*, PMLR 144:1105-1117, 2021.

#### Abstract

Value functions are powerful abstractions broadly used across optimal control and robotics algorithms. Several lines of work have attempted to leverage trajectory optimization to learn value function approximations, usually by solving a large number of trajectory optimization problems as a means to generate training data. Even though these methods point to a promising direction, for sufficiently complex tasks, their sampling requirements can become computationally intractable. In this work, we leverage insights from adversarial learning in order to improve the sampling efficiency of a simple value function learning algorithm. We demonstrate how generating adversarial samples for this task presents a unique challenge due to the loss function that does not admit a closed form expression of the samples, but that instead requires the solution to a nonlinear optimization problem. Our key insight is that by leveraging duality theory from optimization, it is still possible to compute adversarial samples for this learning problem with virtually no computational overhead, including without having to keep track of shifting distributions of approximation errors or having to train generative models. We apply our method, named SEAGuL, to a canonical control task (balancing the acrobot) and a more challenging and highly dynamic nonlinear control task (the perching of a small glider). We demonstrate that compared to random sampling, with the same number of samples, training value function approximations using SEAGuL leads to improved generalization errors that also translate to control performance improvement.