Related papers: Minimal Regret Walras Equilibria for Combinatorial…
Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in…
We consider an assortment selection and pricing problem in which a seller has $N$ different items available for sale. In each round, the seller observes a $d$-dimensional contextual preference information vector for the user, and offers to…
We consider a stochastic multi-armed bandit setting and study the problem of constrained regret minimization over a given time horizon. Each arm is associated with an unknown, possibly multi-dimensional distribution, and the merit of an arm…
This paper presents the first non-asymptotic result showing that a model-free algorithm can achieve a logarithmic cumulative regret for episodic tabular reinforcement learning if there exists a strictly positive sub-optimality gap in the…
Multi-armed Bandit motivates methods with provable upper bounds on regret and also the counterpart lower bounds have been extensively studied in this context. Recently, Multi-agent Multi-armed Bandit has gained significant traction in…
We study the regret performance of Sample Average Approximation (SAA) for data-driven newsvendor problems with general convex inventory costs. In literature, the optimality of SAA has not been fully established under both \alpha-global…
We consider the problem of online learning in Linear Quadratic Control systems whose state transition and state-action transition matrices $A$ and $B$ may be initially unknown. We devise an online learning algorithm and provide guarantees…
Feature-based dynamic pricing is an increasingly popular model of setting prices for highly differentiated products with applications in digital marketing, online sales, real estate and so on. The problem was formally studied as an online…
This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to…
We consider the problem of provably optimal exploration in reinforcement learning for finite horizon MDPs. We show that an optimistic modification to value iteration achieves a regret bound of $\tilde{O}( \sqrt{HSAT} + H^2S^2A+H\sqrt{T})$…
We study the problem of dynamic regret minimization in online convex optimization, in which the objective is to minimize the difference between the cumulative loss of an algorithm and that of an arbitrary sequence of comparators. While the…
We study the stochastic combinatorial semi-bandit problem with unrestricted feedback delays under merit-based fairness constraints. This is motivated by applications such as crowdsourcing, and online advertising, where immediate feedback is…
Regret in stochastic multi-armed bandits traditionally measures the difference between the highest reward and either the arithmetic mean of accumulated rewards or the final reward. These conventional metrics often fail to address fairness…
In practical applications, data is used to make decisions in two steps: estimation and optimization. First, a machine learning model estimates parameters for a structural model relating decisions to outcomes. Second, a decision is chosen to…
In this work, we extend the concept of the $p$-mean welfare objective from social choice theory (Moulin 2004) to study $p$-mean regret in stochastic multi-armed bandit problems. The $p$-mean regret, defined as the difference between the…
The contextual combinatorial semi-bandit problem with linear payoff functions is a decision-making problem in which a learner chooses a set of arms with the feature vectors in each round under given constraints so as to maximize the sum of…
We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and customer makes the purchase among offered products according to an uncapacitated multinomial…
This paper proposes a distributionally robust approach to regret optimal control of discrete-time linear dynamical systems with quadratic costs subject to a stochastic additive disturbance on the state process. The underlying probability…
We study agents communicating over an underlying network by exchanging messages, in order to optimize their individual regret in a common nonstochastic multi-armed bandit problem. We derive regret minimization algorithms that guarantee for…
In this paper, we consider the multi-armed bandit problem with high-dimensional features. First, we prove a minimax lower bound, $\mathcal{O}\big((\log d)^{\frac{\alpha+1}{2}}T^{\frac{1-\alpha}{2}}+\log T\big)$, for the cumulative regret,…