Mini-Batch Risk-Averse Deep Q-Learning: A Robot Navigation Case Study

Abstract

We study the control of Markov decision processes in which the quality of a policy is evaluated by a dynamic, time-consistent Markov risk measure rather than by an expected discounted cost. The main obstacle to combining such measures with reinforcement learning is that a transition risk mapping depends on the transition kernel in a nonlinear way, and therefore cannot be estimated from a single observed transition. We remove this obstacle by employing mini-batch transition risk mappings: the mapping is applied to the empirical measure of $N$ independent next-state samples, and the result is averaged. The resulting mapping is again coherent. However, as an expected value of a function of $N$ next-state values, it admits an unbiased one-sample estimator. We embed this mapping into a double deep Q-network, analyze the two sources of estimation bias that arise, and obtain a risk-averse Q-learning method applicable to state spaces far beyond the reach of tabular schemes. The method is applied to an underwater robot navigation problem, in which a vehicle must visit collection points, gather stochastic information payloads, and deliver them at transmission points, while exposed at each step to the risk of destruction. A hierarchical decomposition delegates path execution to an exact graph search and confines learning to the high-level ``collect or transmit'' decision. A low-dimensional feature map, invariant under the symmetries of the problem, replaces the raw state--configuration encoding. In experiments on $300$ held-out environments, the resulting policies transfer to instance sizes never seen in training, and already $N=2$ reduces the upper semideviation of the outcome distribution while simultaneously improving its mean whenever the simulator is misspecified---an empirical counterpart of the duality between coherent risk measures and distributional robustness.