Related papers: Lookback Prophet Inequalities
We consider online variations of the Pandora's box problem (Weitzman. 1979), a standard model for understanding issues related to the cost of acquiring information for decision-making. Our problem generalizes both the classic Pandora's box…
We study the problem of fairly allocating a set of indivisible goods to multiple agents and focus on the proportionality, which is one of the classical fairness notions. Since proportional allocations do not always exist when goods are…
Direct Preference Optimization (DPO) is a simple and efficient framework that has attracted substantial attention. However, it often struggles to meet its primary objectives -- increasing the generation probability of chosen responses while…
We study the problem of online learning in adversarial bandit problems under a partial observability model called off-policy feedback. In this sequential decision making problem, the learner cannot directly observe its rewards, but instead…
This paper develops a decomposition methodology for common agency games in which each principal's payoff depends on her own outcome and the agent's type, but not on rivals' outcomes. The key step reduces each principal's best-response…
In the classical secretary problem, $n$ ranked items arrive one by one, and each item's rank relative to its predecessors is noted. The observer must select or reject each item as it arrives, with the object of selecting the item of highest…
In the buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to some constraints on the set of accepted bids. Decisions to reject bids are irrevocable, whereas…
In this paper, we study $k$-unit single sample prophet inequalities. A seller has $k$ identical, indivisible items to sell. A sequence of buyers arrive one-by-one, with each buyer's private value for the item, $X_i$, revealed to the seller…
We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack, while the follower chooses a feasible packing maximizing his own profit. The leader's aim is to optimize a linear objective function…
We consider the classical question of predicting binary sequences and study the {\em optimal} algorithms for obtaining the best possible regret and payoff functions for this problem. The question turns out to be also equivalent to the…
Fairness is a major concern in contemporary decision problems. In these situations, the objective is to maximize fairness while preserving the efficacy of the underlying decision-making problem. This paper examines repeated decisions on…
We consider a retailer selling a single product with limited on-hand inventory over a finite selling season. Customer demand arrives according to a Poisson process, the rate of which is influenced by a single action taken by the retailer…
We provide prophet inequality algorithms for online weighted matching in general (non-bipartite) graphs, under two well-studied arrival models, namely edge arrival and vertex arrival. The weight of each edge is drawn independently from an…
In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower…
We consider prophet inequalities for XOS and MPH-$k$ combinatorial auctions and give a simplified proof for the existence of static and anonymous item prices which recover the state-of-the-art competitive ratios. Our proofs make use of a…
The traditional information theoretic approach to studying feedback is to consider ideal instantaneous high-rate feedback of the channel outputs to the encoder. This was acceptable in classical work because the results were negative:…
We consider a setting where $n$ buyers, with combinatorial preferences over $m$ items, and a seller, running a priority-based allocation mechanism, repeatedly interact. Our goal, from observing limited information about the results of these…
We study the problem of allocating indivisible goods among agents with additive valuation functions to achieve both fairness and efficiency under the constraint that each agent receives exactly the same number of goods (the \emph{balanced…
We extend the standard online worst-case model to accommodate past experience which is available to the online player in many practical scenarios. We do this by revealing a random sample of the adversarial input to the online player ahead…
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…