Related papers: Tight Samurai Accountant
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
We finish proving that an irreducible automorphism f of a handlebody is efficient if, and only if, a certain standard pair of dual f--invariant laminations have the geometric tightness property. In a previous paper it was proved that this…
Decision makers routinely use constrained optimization technology to plan and operate complex systems like global supply chains or power grids. In this context, practitioners must assess how close a computed solution is to optimality in…
We prove lower bounds for higher-order methods in smooth non-convex finite-sum optimization. Our contribution is threefold: We first show that a deterministic algorithm cannot profit from the finite-sum structure of the objective, and that…
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
With the end of Moore's law and Dennard scaling, efficient training increasingly requires rethinking data volume. Can we train better models with significantly less data via intelligent subsampling? To explore this, we develop SICKLE, a…
Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For…
Relativizing computations of Turing machines to an oracle is a central concept in the theory of computation, both in complexity theory and in computability theory(!). Inspired by lowness notions from computability theory, Allender…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
Models that can simulate how environments change in response to actions can be used by agents to plan and act efficiently. We improve on previous environment simulators from high-dimensional pixel observations by introducing recurrent…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
Specialization and hierarchical organization are important features of efficient collaboration in economical, artificial, and biological systems. Here, we investigate the hypothesis that both features can be explained by the fact that each…
We use the general formulation of irreversible thermodynamics and study the minimally nonlinear irreversible model of heat engines operating between a time-varying hot heat source of finite size and a cold heat reservoir of infinite size.…
This study proposes a robust estimator for stochastic frontier models by integrating the idea of Basu et al. [1998, Biometrika 85, 549-559] into such models. We verify that the suggested estimator is strongly consistent and asymptotic…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the…
A perfectly rational decision-maker chooses the best action with the highest utility gain from a set of possible actions. The optimality principles that describe such decision processes do not take into account the computational costs of…
Recently, Dallal, Neider, and Tabuada studied a generalization of the classical game-theoretic model used in program synthesis, which additionally accounts for unmodeled intermittent disturbances. In this extended framework, one is…
This paper presents a novel formalization of optimality theory. Unlike previous treatments of optimality in computational linguistics, starting with Ellison (1994), the new approach does not require any explicit marking and counting of…
Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…