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We explore the resolution of claims problems with history. At a given period of time, a group of agents holds claims over an insufficient endowment, as they did in previous periods. The solution to the present-period problem might be…
We consider the age-old problem of allocating items among different agents in a way that is efficient and fair. Two papers, by Dolev et al. and Ghodsi et al., have recently studied this problem in the context of computer systems. Both…
Equality of the second order arithmetic means of two principal ideals does not imply equality of their first order arithmetic means (second order equality cancellation). We provide fairly broad sufficient conditions on one of the principal…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
One of the important yet insufficiently studied subjects in fair allocation is the externality effect among agents. For a resource allocation problem, externalities imply that a bundle allocated to an agent may affect the utilities of other…
In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have…
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
In this paper, we consider a general distributed system with multiple agents who select and then implement actions in the system. The system has an operator with a centralized objective. The agents, on the other hand, are selfinterested and…
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…
In this work, we investigate the application of Taylor expansions in reinforcement learning. In particular, we propose Taylor expansion policy optimization, a policy optimization formalism that generalizes prior work (e.g., TRPO) as a…
We introduce and study a multi-class online resource allocation problem with group fairness guarantees. The problem involves allocating a fixed amount of resources to a sequence of agents, each belonging to a specific group. The primary…
In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…
We establish a discrete operator--theoretic framework for the analysis of implicit Euler and Lie--Trotter splitting schemes for delay differential equations (DDEs). Both schemes are formulated in terms of discrete resolvent operators acting…
Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice, course allocations and residency matches. In some cases, several `items' are given to each participant.…
In dispersive media, dissipation appears in the Schr\"odinger representation of classical Maxwell equations as a sparse diagonal operator occupying an $r$-dimensional subspace. A first order Suzuki-Trotter approximation for the evolution…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
Consider a population of agents who repeatedly compete for awards, as in the case of researchers annually applying for grants. Noise in the selection process may encourage entry of low quality proposals, forcing the principal to commit…
In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however…