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Register a new userLeveraging Good Representations in Linear Contextual Bandits
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Added by
Matteo Pirotta
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The linear contextual bandit literature is mostly focused on the design of efficient learning algorithms for a given representation. However, a contextual bandit problem may admit multiple linear representations, each one with different characteristics that directly impact the regret of the learning algorithm. In particular, recent works showed that there exist good representations for which constant problem-dependent regret can be achieved. In this paper, we first provide a systematic analysis of the different definitions of good representations proposed in the literature. We then propose a novel selection algorithm able to adapt to the best representation in a set of $M$ candidates. We show that the regret is indeed never worse than the regret obtained by running LinUCB on the best representation (up to a $ln M$ factor). As a result, our algorithm achieves constant regret whenever a good representation is available in the set. Furthermore, we show that the algorithm may still achieve constant regret by implicitly constructing a good representation, even when none of the initial representations is good. Finally, we empirically validate our theoretical findings in a number of standard contextual bandit problems.
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We consider the linear contextual bandit problem with resource consumption, in addition to reward generation. In each round, the outcome of pulling an arm is a reward as well as a vector of resource consumptions. The expected values of these outcomes depend linearly on the context of that arm. The budget/capacity constraints require that the total consumption doesnt exceed the budget for each resource. The objective is once again to maximize the total reward. This problem turns out to be a common generalization of classic linear contextual bandits (linContextual), bandits with knapsacks (BwK), and the online stochastic packing problem (OSPP). We present algorithms with near-optimal regret bounds for this problem. Our bounds compare favorably to results on the unstructured version of the problem where the relation between the contexts and the outcomes could be arbitrary, but the algorithm only competes against a fixed set of policies accessible through an optimization oracle. We combine techniques from the work on linContextual, BwK, and OSPP in a nontrivial manner while also tackling new difficulties that are not present in any of these special cases.
In this paper, we consider online learning in generalized linear contextual bandits where rewards are not immediately observed. Instead, rewards are available to the decision-maker only after some delay, which is unknown and stochastic. We study the performance of two well-known algorithms adapted to this delayed setting: one based on upper confidence bounds, and the other based on Thompson sampling. We describe modifications on how these two algorithms should be adapted to handle delays and give regret characterizations for both algorithms. Our results contribute to the broad landscape of contextual bandits literature by establishing that both algorithms can be made to be robust to delays, thereby helping clarify and reaffirm the empirical success of these two algorithms, which are widely deployed in modern recommendation engines.
Standard approaches to decision-making under uncertainty focus on sequential exploration of the space of decisions. However, textit{simultaneously} proposing a batch of decisions, which leverages available resources for parallel experimentation, has the potential to rapidly accelerate exploration. We present a family of (parallel) contextual linear bandit algorithms, whose regret is nearly identical to their perfectly sequential counterparts -- given access to the same total number of oracle queries -- up to a lower-order burn-in term that is dependent on the context-set geometry. We provide matching information-theoretic lower bounds on parallel regret performance to establish our algorithms are asymptotically optimal in the time horizon. Finally, we also present an empirical evaluation of these parallel algorithms in several domains, including materials discovery and biological sequence design problems, to demonstrate the utility of parallelized bandits in practical settings.
Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical performance compared to the state-of-the-art methods. However, many questions regarding its theoretical performance remained open. In this paper, we design and analyze a generalization of Thompson Sampling algorithm for the stochastic contextual multi-armed bandit problem with linear payoff functions, when the contexts are provided by an adaptive adversary. This is among the most important and widely studi
Contextual bandits are widely used in Internet services from news recommendation to advertising, and to Web search. Generalized linear models (logistical regression in particular) have demonstrated stronger performance than linear models in many applications where rewards are binary. However, most theoretical analyses on contextual bandits so far are on linear bandits. In this work, we propose an upper confidence bound based algorithm for generalized linear contextual bandits, which achieves an $tilde{O}(sqrt{dT})$ regret over $T$ rounds with $d$ dimensional feature vectors. This regret matches the minimax lower bound, up to logarithmic terms, and improves on the best previous result by a $sqrt{d}$ factor, assuming the number of arms is fixed. A key component in our analysis is to establish a new, sharp finite-sample confidence bound for maximum-likelihood estimates in generalized linear models, which may be of independent interest. We also analyze a simpler upper confidence bound algorithm, which is useful in practice, and prove it to have optimal regret for certain cases.
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