Related papers: On Bellman's principle with inequality constraints
We study a Markov decision problem in which the state space is the set of finite marked point configurations in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the…
A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…
Bell's inequalities, in the form given by Cerf and Adami, are derived from the combination of the second law of thermodynamics and the Markov postulate. Violations of these inequalities are discussed in terms of the mixing characteristics…
We present a prescription for obtaining Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give examples of some families of such inequalities. The inequalities are violated by certain classes…
The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decision-making by economic agents. In the average-cost optimal control…
Markov decision problems are most commonly solved via dynamic programming. Another approach is Bellman residual minimization, which directly minimizes the squared Bellman residual objective function. However, compared to dynamic…
Optimization of decision problems in stochastic environments is usually concerned with maximizing the probability of achieving the goal and minimizing the expected episode length. For interacting agents in time-critical applications,…
We study the relation between violation of Bell inequalities and distillability properties of quantum states. Recently, D\"ur has shown that there are some multiparticle bound entangled states, non-separable and non-distillable, that…
The violation of a Bell inequality is an experimental observation that forces one to abandon a local realistic worldview, namely, one in which physical properties are (probabilistically) defined prior to and independent of measurement and…
We study limiting trace inequalities in the style of Maz'ya and Meyers--Ziemer for Sobolev martingales. We develop the Bellman function approach to such estimates, which allows to provide sufficient and almost necessary conditions on the…
In this paper, we consider risk-sensitive discounted control problem for continuous-time jump Markov processes taking values in general state space. The transition rates of underlying continuous-time jump Markov processes and the cost rates…
We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly…
In the present paper, the maximum principle for finite horizon state constrained problems from the book by R. Vinter [\textit{Optimal Control}, Birkh\"auser, Boston, 2000; Theorem~9.3.1] is analyzed via parametric examples. The latter has…
In this work, we study the use of the Bellman equation as a surrogate objective for value prediction accuracy. While the Bellman equation is uniquely solved by the true value function over all state-action pairs, we find that the Bellman…
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR…
We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation…
We prove that for every Bell's inequality and for a broad class of protocols, there always exists a multi-party communication complexity problem, for which the protocol assisted by states which violate the inequality is more efficient than…
We report the measurement of a Bell inequality violation with a single atom and a single photon prepared in a probabilistic entangled state. This is the first demonstration of such a violation with particles of different species. The…
The Bounded Real Lemma, i.e., the state-space linear matrix inequality characterization (referred to as Kalman-Yakubovich-Popov or KYP inequality) of when an input/state/output linear system satisfies a dissipation inequality, has recently…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…