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   Jiaohao Zheng, Mehmet Necip (January 2021, ICANN 2021)

   I. Farkaˇs et al. (Ed.)

   We propose a new deep deterministic actor-critic algorithm with an integrated network architecture and an integrated objective func- tion. We address stabilization of the learning procedure via a novel adap- tive objective that roughly ensures keeping the actor unchanged while the critic makes large errors. We reduce the number of network parame- ters and propose an improved exploration strategy over bounded action spaces. Moreover, we incorporate some recent advances in deep learn- ing to our algorithm. Experiments illustrate that our algorithm speeds up the learning process and reduces the sample complexity considerably over the state-of-the-art algorithms including TD3, SAC, PPO, and A2C in continuous control tasks. 

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2. Empirical Q-Value Iteration

   https://doi.org/10.1287/stsy.2019.0062  

   Kalathil, Dileep; Borkar, Vivek S.; Jain, Rahul (October 2020, Stochastic Systems)

   null (Ed.)

   We propose a new simple and natural algorithm for learning the optimal Q-value function of a discounted-cost Markov decision process (MDP) when the transition kernels are unknown. Unlike the classical learning algorithms for MDPs, such as Q-learning and actor-critic algorithms, this algorithm does not depend on a stochastic approximation-based method. We show that our algorithm, which we call the empirical Q-value iteration algorithm, converges to the optimal Q-value function. We also give a rate of convergence or a nonasymptotic sample complexity bound and show that an asynchronous (or online) version of the algorithm will also work. Preliminary experimental results suggest a faster rate of convergence to a ballpark estimate for our algorithm compared with stochastic approximation-based algorithms. 

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3. Provable Policy Gradient Methods for Average-Reward Markov Potential Games

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   We study Markov potential games under the infinite horizon average reward criterion. Most previous studies have been for discounted rewards. We prove that both algorithms based on independent policy gradient and independent natural policy gradient converge globally to a Nash equilibrium for the average reward criterion. To set the stage for gradient-based methods, we first establish that the average reward is a smooth function of policies and provide sensitivity bounds for the differential value functions, under certain conditions on ergodicity and the second largest eigenvalue of the underlying Markov decision process (MDP). We prove that three algorithms, policy gradient, proximal-Q, and natural policy gradient (NPG), converge to an ϵ-Nash equilibrium with time complexity O(1ϵ2), given a gradient/differential Q function oracle. When policy gradients have to be estimated, we propose an algorithm with ~O(1mins,aπ(a|s)δ) sample complexity to achieve δ approximation error w.r.t~the ℓ2 norm. Equipped with the estimator, we derive the first sample complexity analysis for a policy gradient ascent algorithm, featuring a sample complexity of ~O(1/ϵ5). Simulation studies are presented. 

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4. Actor-Critic PAC Robust Policy Search

   Sheckells, Matthew; Garimella, Gowtham; Michra, Subhransu; Kobilarov, Marin (May 2019, ICRA 2019)

   This work studies an approach for computing provably robust control laws for robotic systems operating in uncertain environments. We develop an actor-critic style policy search algorithm based on the idea of minimizing an upper confidence bound on the negative expected advantage of a control policy at each policy update iteration. This new algorithm is a reformulation of Probably-Approximately-Correct Robust Policy Search (PROPS) and, unlike PROPS, allows for both step-based evaluation and step-based sampling strategies in policy parameter space, enabled by the use of Generalized Advantage Estimation and Generalized Exploration. As a result, the new algorithm is more data efficient and is expected to compute higher quality policies faster. We empirically evaluate the algorithm in simulation on a challenging robot navigation task using a high-fidelity deep stochastic model of an agile ground vehicle and compare its performance to the original trajectory-based PROPS 

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5. Sampling Multiple Edges Efficiently

   Eden, T.; Mossel, S.; Rubinfeld, R. (January 2021, Random)

   We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise ϵ-close to the uniform distribution, in an amortized-efficient fashion. We consider the adjacency list query model, where access to a graph G is given via degree and neighbor queries. The problem of sampling a single edge in this model has been raised by Eden and Rosenbaum (SOSA 18). Let n and m denote the number of vertices and edges of G, respectively. Eden and Rosenbaum provided upper and lower bounds of Θ∗(n/ √ m) for sampling a single edge in general graphs (where O ∗(·) suppresses poly(1/ϵ) and poly(log n) dependencies). We ask whether the query complexity lower bound for sampling a single edge can be circumvented when multiple samples are required. That is, can we get an improved amortized per-sample cost if we allow a preprocessing phase? We answer in the affirmative. We present an algorithm that, if one knows the number of required samples q in advance, has an overall cost that is sublinear in q, namely, O∗(√ q · (n/ √ m)), which is strictly preferable to O∗(q · (n/ √ m)) cost resulting from q invocations of the algorithm by Eden and Rosenbaum. Subsequent to a preliminary version of this work, Tětek and Thorup (arXiv, preprint) proved that this bound is essentially optimal. 

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