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Ben Berger

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3 papers

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AIJ Journal 2025 Journal Article

Pandora's box problem with time constraints

Georgios Amanatidis
Ben Berger
Tomer Ezra
Michal Feldman
Federico Fusco
Rebecca Reiffenhäuser
Artem Tsikiridis

The Pandora's Box problem models the search for the best alternative when evaluation is costly. In the simplest variant, a decision maker is presented with $n$ boxes, each associated with a cost of inspection and a hidden random reward. The decision maker inspects a subset of these boxes one after the other, in a possibly adaptive order, and gains the difference between the largest revealed reward and the sum of the inspection costs. Although this classic version is well understood (Weitzman 1979), there is a flourishing recent literature on variants of the problem. Here we introduce a general framework -- the Pandora's Box Over Time problem -- that captures a wide range of variants where time plays a role, e. g. , by constraining the schedules of exploration and influencing costs and rewards. In our framework, boxes have time-dependent rewards and costs, whereas inspection may require a box-specific processing time. Moreover, once a box is inspected, its reward may deteriorate over time. Our main result is an efficient constant-factor approximation to the optimal strategy for the Pandora's Box Over Time problem, which is generally NP-hard to compute. We further obtain improved results for the natural special cases where boxes have no processing time, boxes are available only in specific time slots, or when costs and reward distributions are time-independent (but rewards may still deteriorate after inspection).

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AAAI Conference 2024 Conference Paper

Pandora’s Problem with Deadlines

Ben Berger
Tomer Ezra
Michal Feldman
Federico Fusco

Pandora’s problem is a fundamental model that studies optimal search under costly inspection. In the classic version, there are n boxes, each associated with a known cost and a known distribution over values. A strategy inspects the boxes sequentially and obtains a utility that equals the difference between the maximum value of an inspected box and the total inspection cost. Weitzman (1979) presented a surprisingly simple strategy that obtains the optimal expected utility. In this work we introduce a new variant of Pandora’s problem in which every box is also associated with a publicly known deadline, indicating the final round by which its value may be chosen. This model captures many real-life scenarios where alternatives admit deadlines, such as candidate interviews and college admissions. Our main result is an efficient threshold-based strategy that achieves a constant approximation relative to the performance of the optimal strategy for the deadlines setting.

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AAAI Conference 2022 Conference Paper

Almost Full EFX Exists for Four Agents

Ben Berger
Avi Cohen
Michal Feldman
Amos Fiat

The existence of EFX allocations of goods is a major open problem in fair division, even for additive valuations. The current state of the art is that no setting where EFX allocations are impossible is known, and yet, existence results are known only for very restricted settings, such as: (i) agents with identical valuations, (ii) 2 agents, and (iii) 3 agents with additive valuations. It is also known that EFX exists if one can leave n − 1 items unallocated, where n is the number of agents. We develop new techniques that allow us to push the boundaries of the enigmatic EFX problem beyond these known results, and (arguably) to simplify proofs of earlier results. Our main result is that every setting with 4 additive agents admits an EFX allocation that leaves at most a single item unallocated. Beyond our main result, we introduce a new class of valuations, termed nice cancelable, which includes additive, unit-demand, budget-additive and multiplicative valuations, among others. Using our new techniques, we show that both our results and previous results for additive valuations extend to nice cancelable valuations.

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