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We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies, whose expected cumulative reward over the course of $T$ rounds is maximum, and each has an expected cost below a certain threshold $tau$. We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB), and prove an $widetilde{mathcal{O}}(frac{dsqrt{T}}{tau-c_0})$ bound on its $T$-round regret, where the denominator is the difference between the constraint threshold and the cost of a known feasible action. We further specialize our results to multi-armed bandits and propose a computationally efficient algorithm for this setting. We prove a regret bound of $widetilde{mathcal{O}}(frac{sqrt{KT}}{tau - c_0})$ for this algorithm in $K$-armed bandits, which is a $sqrt{K}$ improvement over the regret bound we obtain by simply casting multi-armed bandits as an instance of contextual linear bandits and using the regret bound of OPLB. We also prove a lower-bound for the problem studied in the paper and provide simulations to validate our theoretical results.
Bandit algorithms have various application in safety-critical systems, where it is important to respect the system constraints that rely on the bandits unknown parameters at every round. In this paper, we formulate a linear stochastic multi-armed ban
We study decentralized stochastic linear bandits, where a network of $N$ agents acts cooperatively to efficiently solve a linear bandit-optimization problem over a $d$-dimensional space. For this problem, we propose DLUCB: a fully decentralized algor
We propose a new online algorithm for minimizing the cumulative regret in stochastic linear bandits. The key idea is to build a perturbed history, which mixes the history of observed rewards with a pseudo-history of randomly generated i.i.d. pseudo-r
In the stochastic linear contextual bandit setting there exist several minimax procedures for exploration with policies that are reactive to the data being acquired. In practice, there can be a significant engineering overhead to deploy these algorit
Modifying the reward-biased maximum likelihood method originally proposed in the adaptive control literature, we propose novel learning algorithms to handle the explore-exploit trade-off in linear bandits problems as well as generalized linear bandit