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Gaussian Mixture Models (GMMs) have been recently proposed for approximating actors in actor-critic reinforcement learning algorithms. Such GMM-based actors are commonly optimized using stochastic policy gradients along with an entropy maximization objective. In contrast to previous work, we define and study deterministic policy gradients for optimiz- ing GMM-based actors. Similar to stochastic gradient approaches, our proposed method, denoted Gaussian Mixture Deterministic Policy Gradient (Gamid-PG), encourages policy entropy maximization. To this end, we define the GMM entropy gradient using Varia- tional Approximation of the KL-divergence between the GMM’s component Gaussians. We compare Gamid-PG with common stochastic policy gradient methods on benchmark dense- reward MuJoCo tasks and sparse-reward Fetch tasks. We observe that Gamid-PG outper- forms stochastic gradient-based methods in 3/6 MuJoCo tasks while performing similarly on the remaining 3 tasks. In the Fetch tasks, Gamid-PG outperforms single-actor determinis- tic gradient-based methods while performing worse than stochastic policy gradient methods. Consequently, we conclude that GMMs optimized using deterministic policy gradients (1) should be favorably considered over stochastic gradients in dense-reward continuous control tasks, and (2) improve upon single-actor deterministic gradients. 

Comprehensive state-action exploration is essential for reinforcement learning (RL) algorithms. It enables them to find optimal solutions and avoid premature convergence. In value-based RL, optimistic initialization of the value function ensures sufficient exploration for finding the optimal solution. Optimistic values lead to curiosity-driven exploration enabling visitation of under-explored regions. However, optimistic initialization has limitations in stochastic and non-stationary environments due to its inability to explore ''infinitely-often''. To address this limitation, we propose a novel exploration strategy for value-based RL, denoted COIN, based on recurring optimistic initialization. By injecting a continual exploration bonus, we overcome the shortcoming of optimistic initialization (sensitivity to environment noise). We provide a rigorous theoretical comparison of COIN versus existing popular exploration strategies and prove it provides a unique set of attributes (coverage, infinite-often, no visitation tracking, and curiosity). We demonstrate the superiority of COIN over popular existing strategies on a designed toy domain as well as present results on common benchmark tasks. We observe that COIN outperforms existing exploration strategies in four out of six benchmark tasks while performing on par with the best baseline on the other two tasks.