Related papers: Tight Samurai Accountant
We say that a theory $T$ is intermediate under effective reducibility if the isomorphism problems among its computable models is neither hyperarithmetic nor on top under effective reducibility. We prove that if an infinitary sentence $T$ is…
Stochastic approximation (SA) is an iterative algorithm for finding the fixed point of an operator using noisy samples and widely used in optimization and Reinforcement Learning (RL). The noise in RL exhibits a Markovian structure, and in…
In this paper, we propose a new constraint, called shift-consistency, for solving matrix/tensor completion problems in the context of recommender systems. Our method provably guarantees several key mathematical properties: (1) satisfies a…
The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by…
Our goal is to solve both problems of adverse selection and moral hazard for multi-agent projects. In our model, each selected agent can work according to his private "capability tree". This means a process involving hidden actions, hidden…
A principal must decide between two options. Which one she prefers depends on the private information of two agents. One agent always prefers the first option; the other always prefers the second. Transfers are infeasible. One application…
How does one allocate a collection of resources to a set of strategic agents in a fair and efficient manner without using money? For in many scenarios it is not feasible to use money to compensate agents for otherwise unsatisfactory…
We introduce a new consistency-based approach for defining and solving nonnegative/positive matrix and tensor completion problems. The novelty of the framework is that instead of artificially making the problem well-posed in the form of an…
Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…
A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify robust natural distributed algorithms that converge quickly to an equilibrium.…
The internal structure and operation mechanism of large-scale language models are analyzed theoretically, especially how Transformer and its derivative architectures can restrict computing efficiency while capturing long-term dependencies.…
Guarded protocols were introduced in a seminal paper by Emerson and Kahlon (2000), and describe systems of processes whose transitions are enabled or disabled depending on the existence of other processes in certain local states. We study…
The higher than classical efficiency exhibited by some quantum algorithms is here ascribed to their non-mechanistic character, which becomes evident by joining the notions of entanglement and quantum measurement. Measurement analogically…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
The interplay of optimizers and architectures in neural networks is complicated and hard to understand why some optimizers work better on some specific architectures. In this paper, we find that the traditionally used sharpness metric does…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
This paper studies a one-sector optimal growth model with i.i.d. productivity shocks that are allowed to be unbounded. The utility function is assumed to be non-negative and unbounded from above. The novel feature in our framework is that…
Resilient algorithms in high-performance computing are subject to rigorous non-functional constraints. Resiliency must not increase the runtime, memory footprint or I/O demands too significantly. We propose a task-based soft error detection…
General criterion for best efficiency of the interaction of a complex system with an ever-changing environment is derived. Its exclusive property, set by boundedness, is that the highly non-trivial interplay between parameters that…
This paper addresses a fundamental and important question in control: under what conditions does there fail to exist a robust control policy that keeps the state of a constrained linear system within a target set, despite bounded…