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We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the optimal strategy. The exact blackjack…
We study the optimal allocation of prizes in rank-order tournaments with loss averse agents. Prize sharing becomes increasingly optimal with loss aversion because more equitable prizes reduce the marginal psychological cost of anticipated…
We consider the problem of best arm identification in a variant of multi-armed bandits called linked bandits. In a single interaction with linked bandits, multiple arms are played sequentially until one of them receives a positive reward.…
Contextual dueling bandit is used to model the bandit problems, where a learner's goal is to find the best arm for a given context using observed noisy human preference feedback over the selected arms for the past contexts. However,…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
Unsupervised skill learning objectives (Gregor et al., 2016, Eysenbach et al., 2018) allow agents to learn rich repertoires of behavior in the absence of extrinsic rewards. They work by simultaneously training a policy to produce…
This paper studies the design of optimal proper scoring rules when the principal has partial knowledge of an agent's signal distribution. Recent work characterizes the proper scoring rules that maximize the increase of an agent's payoff…
Reward machines allow the definition of rewards for temporally extended tasks and behaviors. Specifying "informative" reward machines can be challenging. One way to address this is to generate reward machines from a high-level abstract…
In this work, we initiate the study of fault tolerant Max Cut, where given an edge-weighted undirected graph $G=(V,E)$, the goal is to find a cut $S\subseteq V$ that maximizes the total weight of edges that cross $S$ even after an adversary…
We study the problem of best-arm identification with fixed confidence in stochastic linear bandits. The objective is to identify the best arm with a given level of certainty while minimizing the sampling budget. We devise a simple algorithm…
Algorithms for hyperparameter optimization abound, all of which work well under different and often unverifiable assumptions. Motivated by the general challenge of sequentially choosing which algorithm to use, we study the more specific…
We propose a new problem setting to study the sequential interactions between a recommender system and a user. Instead of assuming the user is omniscient, static, and explicit, as the classical practice does, we sketch a more realistic user…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
Inverse reinforcement learning (IRL) seeks to learn the reward function from expert trajectories, to understand the task for imitation or collaboration thereby removing the need for manual reward engineering. However, IRL in the context of…
We investigate the benefits of heterogeneity in multi-agent explore-exploit decision making where the goal of the agents is to maximize cumulative group reward. To do so we study a class of distributed stochastic bandit problems in which…
This paper considers the multi-armed thresholding bandit problem -- identifying all arms whose expected rewards are above a predefined threshold via as few pulls (or rounds) as possible -- proposed by Locatelli et al. [2016] recently.…
Motivated by applications such as online labor markets we consider a variant of the stochastic multi-armed bandit problem where we have a collection of arms representing strategic agents with different performance characteristics. The…
Proper scoring rules incentivize experts to accurately report beliefs, assuming predictions cannot influence outcomes. We relax this assumption and investigate incentives when predictions are performative, i.e., when they can influence the…
We study a grouped bandit setting where each arm comprises multiple independent sub-arms referred to as attributes. Each attribute of each arm has an independent stochastic reward. We impose the constraint that for an arm to be deemed…
We consider the problem of a learning agent who has to repeatedly play a general sum game against a strategic opponent who acts to maximize their own payoff by optimally responding against the learner's algorithm. The learning agent knows…