Related papers: Minimizing the time to a decision
We investigated the unbounded diffusion observed in a time-dependent oval-shaped billiard and its suppression owing to inelastic collisions with the boundary. The main focus is on the behavior of the diffusion coefficient, which plays a key…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
In simple perceptual decisions the brain has to identify a stimulus based on noisy sensory samples from the stimulus. Basic statistical considerations state that the reliability of the stimulus information, i.e., the amount of noise in the…
Imagine a large firm with multiple departments that plans a large recruitment. Candidates arrive one-by-one, and for each candidate the firm decides, based on her data (CV, skills, experience, etc), whether to summon her for an interview.…
We study the long-term behavior of the two-thinning variant of the classical balls-and-bins model. In this model, an overseer is provided with uniform random allocation of $m$ balls into $n$ bins in an on-line fashion. For each ball, the…
Recent progress in Quality Diversity Reinforcement Learning (QD-RL) has enabled learning a collection of behaviorally diverse, high performing policies. However, these methods typically involve storing thousands of policies, which results…
We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the…
Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these…
Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…
Different approaches are presented to investigate diffusion from a point source in a slab delimited by two absorbing boundaries consisting of parallel infinite planes. These approaches enable to consider the effect of absorption at the…
The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the…
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
Scenario decision making offers a flexible way of making decision in an uncertain environment while obtaining probabilistic guarantees on the risk of failure of the decision. The idea of this approach is to draw samples of the uncertainty…
In this paper, we study the problem of estimating uniformly well the mean values of several distributions given a finite budget of samples. If the variance of the distributions were known, one could design an optimal sampling strategy by…
We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naive agents who reoptimize continuously in time, as well as equilibrium strategies…
A class of generalized exclusion processes parametrized by the maximal occupancy, $k\geq 1$, is investigated. For these processes with symmetric nearest-neighbor hopping, we compute the diffusion coefficient and show that it is independent…
Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Offline planning often struggles with poor sampling efficiency as it tries to learn policies from scratch. Especially with diffusion models, such cold start practices mean that both training and sampling become very expensive. We…