Related papers: On Submodular Prophet Inequalities and Correlation…
The prophet inequality is one of the cornerstone problems in optimal stopping theory and has become a crucial tool for designing sequential algorithms in Bayesian settings. In the i.i.d. $k$-selection prophet inequality problem, we…
Due to numerous applications in retail and (online) advertising the problem of assortment selection has been widely studied under many combinations of discrete choice models and feasibility constraints. In many situations, however, an…
We study online selection problems in both the prophet and secretary settings, when arriving agents have interdependent values. In the interdependent values model, introduced in the seminal work of Milgrom and Weber [1982], each agent has a…
Prophet inequalities are a useful tool for designing online allocation procedures and comparing their performance to the optimal offline allocation. In the basic setting of $k$-unit prophet inequalities, the well-known procedure of Alaei…
We introduce a variant of the classic prophet inequality, called \emph{residual prophet inequality} (RPI). In the RPI problem, we consider a finite sequence of $n$ nonnegative independent random values with known distributions, and a known…
Temporal prefetching shows promise for handling irregular memory access patterns, which are common in data-dependent and pointer-based data structures. Recent studies introduced on-chip metadata storage to reduce the memory traffic caused…
We study threshold testing, an elementary probing model with the goal to choose a large value out of $n$ i.i.d. random variables. An algorithm can test each variable $X_i$ once for some threshold $t_i$, and the test returns binary feedback…
This work introduces \emph{sharding} and \emph{Poissonization} as a unified framework for analyzing prophet inequalities. Sharding involves splitting a random variable into several independent random variables, shards, that collectively…
The secretary problem is one of the fundamental problems in online decision making; a tight competitive ratio for this problem of $1/\mathrm{e} \approx 0.368$ has been known since the 1960s. Much more recently, the study of algorithms with…
Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race.…
We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single sample from each distribution. When the distributions are…
This note records a common threshold/surplus decomposition for single-threshold stopping rules in the classical prophet inequality. The same decomposition is used to certify several deterministic thresholds, including the median, half-mean,…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
Cumulative constraints are central in scheduling with constraint programming, yet propagation is typically performed per constraint, missing multi-resource interactions and causing severe slowdowns on some benchmarks. I present a…
We enable efficient and effective coordination in unpredictable environments, i.e., in environments whose future evolution is unknown a priori and even adversarial. We are motivated by the future of autonomy that involves multiple robots…
We develop a new framework for designing online policies given access to an oracle providing statistical information about an offline benchmark. Having access to such prediction oracles enables simple and natural Bayesian selection…
Information inequalities appear in many database applications such as query output size bounds, query containment, and implication between data dependencies. Recently Khamis et al. proposed to study the algorithmic aspects of information…
Optimization of DR-submodular functions has experienced a notable surge in significance in recent times, marking a pivotal development within the domain of non-convex optimization. Motivated by real-world scenarios, some recent works have…
The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…
We study online prediction where regret of the algorithm is measured against a benchmark defined via evolving constraints. This framework captures online prediction on graphs, as well as other prediction problems with combinatorial…