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تسجيل مستخدم جديدParallelizing Thompson Sampling
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How can we make use of information parallelism in online decision making problems while efficiently balancing the exploration-exploitation trade-off? In this paper, we introduce a batch Thompson Sampling framework for two canonical online decision making problems, namely, stochastic multi-arm bandit and linear contextual bandit with finitely many arms. Over a time horizon $T$, our textit{batch} Thompson Sampling policy achieves the same (asymptotic) regret bound of a fully sequential one while carrying out only $O(log T)$ batch queries. To achieve this exponential reduction, i.e., reducing the number of interactions from $T$ to $O(log T)$, our batch policy dynamically determines the duration of each batch in order to balance the exploration-exploitation trade-off. We also demonstrate experimentally that dynamic batch allocation dramatically outperforms natural baselines such as static batch allocations.
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In this paper, we propose a Thompson Sampling algorithm for emph{unimodal} bandits, where the expected reward is unimodal over the partially ordered arms. To exploit the unimodal structure better, at each step, instead of exploration from the entire
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Bayesian optimization (BO) is a prominent approach to optimizing expensive-to-evaluate black-box functions. The massive computational capability of edge devices such as mobile phones, coupled with privacy concerns, has led to a surging interest in fe
derated learning (FL) which focuses on collaborative training of deep neural networks (DNNs) via first-order optimization techniques. However, some common machine learning tasks such as hyperparameter tuning of DNNs lack access to gradients and thus require zeroth-order/black-box optimization. This hints at the possibility of extending BO to the FL setting (FBO) for agents to collaborate in these black-box optimization tasks. This paper presents federated Thompson sampling (FTS) which overcomes a number of key challenges of FBO and FL in a principled way: We (a) use random Fourier features to approximate the Gaussian process surrogate model used in BO, which naturally produces the parameters to be exchanged between agents, (b) design FTS based on Thompson sampling, which significantly reduces the number of parameters to be exchanged, and (c) provide a theoretical convergence guarantee that is robust against heterogeneous agents, which is a major challenge in FL and FBO. We empirically demonstrate the effectiveness of FTS in terms of communication efficiency, computational efficiency, and practical performance.
We study Thompson sampling (TS) in online decision-making problems where the uncertain environment is sampled from a mixture distribution. This is relevant to multi-task settings, where a learning agent is faced with different classes of problems. We
incorporate this structure in a natural way by initializing TS with a mixture prior -- dubbed MixTS -- and develop a novel, general technique for analyzing the regret of TS with such priors. We apply this technique to derive Bayes regret bounds for MixTS in both linear bandits and tabular Markov decision processes (MDPs). Our regret bounds reflect the structure of the problem and depend on the number of components and confidence width of each component of the prior. Finally, we demonstrate the empirical effectiveness of MixTS in both synthetic and real-world experiments.
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