Efficient Algorithms for Mitigating Uncertainty and Risk in Reinforcement Learning
This dissertation makes three main contributions. First, We identify a new connection between policy gradient and dynamic programming in MMDPs and propose the Coordinate Ascent Dynamic Programming (CADP) algorithm to compute a Markov policy that maximizes the discounted return averaged over the uncertain models. CADP adjusts model weights iteratively to guarantee monotone policy improvements to a local maximum. Second, We establish sufficient and necessary conditions for the exponential ERM Bellman operator to be a contraction and prove the existence of stationary deterministic optimal policies for ERM-TRC and EVaR-TRC. We also propose exponential value iteration, policy iteration, and linear programming algorithms for computing optimal stationary policies for ERM-TRC and EVaR-TRC. Third, We propose model-free Q-learning algorithms for computing policies with risk-averse objectives: ERM-TRC and EVaR-TRC. The challenge is that Q-learning ERM Bellman may not be a contraction. Instead, we use the monotonicity of Q-learning ERM Bellman operators to derive a rigorous proof that the ERM-TRC and the EVaR-TRC Q-learning algorithms converge to the optimal risk-averse value functions. The proposed Q-learning algorithms compute the optimal stationary policy for ERM-TRC and EVaR-TRC.
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