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Register a new userPolicy Gradient Optimization of Thompson Sampling Policies
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Seungki Min
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We study the use of policy gradient algorithms to optimize over a class of generalized Thompson sampling policies. Our central insight is to view the posterior parameter sampled by Thompson sampling as a kind of pseudo-action. Policy gradient methods can then be tractably applied to search over a class of sampling policies, which determine a probability distribution over pseudo-actions (i.e., sampled parameters) as a function of observed data. We also propose and compare policy gradient estimators that are specialized to Bayesian bandit problems. Numerical experiments demonstrate that direct policy search on top of Thompson sampling automatically corrects for some of the algorithms known shortcomings and offers meaningful improvements even in long horizon problems where standard Thompson sampling is extremely effective.
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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 federated 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.
Policy gradient methods have shown success in learning control policies for high-dimensional dynamical systems. Their biggest downside is the amount of exploration they require before yielding high-performing policies. In a lifelong learning setting, in which an agent is faced with multiple consecutive tasks over its lifetime, reusing information from previously seen tasks can substantially accelerate the learning of new tasks. We provide a novel method for lifelong policy gradient learning that trains lifelong function approximators directly via policy gradients, allowing the agent to benefit from accumulated knowledge throughout the entire training process. We show empirically that our algorithm learns faster and converges to better policies than single-task and lifelong learning baselines, and completely avoids catastrophic forgetting on a variety of challenging domains.
Wireless communication systems operate in complex time-varying environments. Therefore, selecting the optimal configuration parameters in these systems is a challenging problem. For wireless links, emph{rate selection} is used to select the optimal data transmission rate that maximizes the link throughput subject to an application-defined latency constraint. We model rate selection as a stochastic multi-armed bandit (MAB) problem, where a finite set of transmission rates are modeled as independent bandit arms. For this setup, we propose Con-TS, a novel constrained version of the Thompson sampling algorithm, where the latency requirement is modeled by a high-probability linear constraint. We show that for Con-TS, the expected number of constraint violations over T transmission intervals is upper bounded by O(sqrt{KT}), where K is the number of available rates. Further, the expected loss in cumulative throughput compared to the optimal rate selection scheme (i.e., the egret is also upper bounded by O(sqrt{KT log K}). Through numerical simulations, we demonstrate that Con-TS significantly outperforms state-of-the-art bandit schemes for rate selection.
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.
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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