| 1. |
- Charalambous, Charalambos D., et al.
(författare)
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Dynamic programming with total variational distance uncertaint
- 2012
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Ingår i: Decision and Control (CDC), 2012 IEEE 51st Annual Conference on. - : IEEE. ; , s. 1909-1914
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Konferensbidrag (refereegranskat)abstract
- The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variational distance uncertainty on the conditional distribution of the controlled process. Utilizing concepts from signed measures, the maximization of a linear functional on the space of probability measures on abstract spaces is investigated, among those probability measures which are within a total variational distance from a nominal probability measure. The maximizing probability measure is found in closed form. These results are then applied to solve minimax stochastic control with deterministic control strategies, under a Markovian assumption on the conditional distributions of the controlled process. The results include: 1) Optimization subject to total variational distance constraints, 2) new dynamic programming recursions, which involve the oscillator seminorm of the value function.
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| 2. |
- Charalambous, Charalambos D., et al.
(författare)
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Extremum Problems with Total Variation Distance
- 2013
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Ingår i: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). - : IEEE conference proceedings. - 9781467357142 ; , s. 1204-1209
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Konferensbidrag (refereegranskat)abstract
- The aim of this paper is to investigate extremum problems with pay-off the total variational distance metric subject to linear functional constraints both defined on the space of probability measures, as well as related problems. Utilizing concepts from signed measures, the extremum probability measures of such problems are obtained in closed form, by identifying the partition of the support set and the mass of these extremum measures on the partition. The results are derived for abstract spaces, specifically, complete separable metric spaces, while the high level ideas are also discussed for denumerable spaces endowed with the discrete topology.
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| 3. |
- Charalambous, Charalambos D., et al.
(författare)
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Extremum Problems With Total Variation Distance and Their Applications
- 2014
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 59:9, s. 2353-2368
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to investigate extremum problems with pay-off being the total variation distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures, and vice-versa; that is, with the roles of total variation metric and linear functional interchanged. Utilizing concepts from signed measures, the extremum probability measures of such problems are obtained in closed form, by identifying the partition of the support set and the mass of these extremum measures on the partition. The results are derived for abstract spaces; specifically, complete separable metric spaces known as Polish spaces, while the high level ideas are also discussed for denumerable spaces endowed with the discrete topology. These extremum problems often arise in many areas, such as, approximating a family of probability distributions by a given probability distribution, maximizing or minimizing entropy subject to total variation distance metric constraints, quantifying uncertainty of probability distributions by total variation distance metric, stochastic minimax control, and in many problems of information, decision theory, and minimax theory.
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| 4. |
- Charalambous, Charalambos D., et al.
(författare)
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Team Optimality Conditions of Differential Decision Systems with Nonclasssical Information Structures
- 2014
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Ingår i: 2014 European Control Conference (ECC). - : IEEE. - 9783952426913 ; , s. 2851-2856
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Konferensbidrag (refereegranskat)abstract
- We derive team optimality conditions for differential decision systems with nonclassical information structures. The necessary conditions of optimality are given in terms of Hamiltonian system of equations consisting of a coupled backward and forward differential equations and a Hamiltonian projected onto the subspace generated by the information structures. Under certain global convexity conditions it is shown that person-by-person optimality implies team optimality.
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| 5. |
- Charalambous, Themistoklis, et al.
(författare)
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Optimal Merging Algorithms for Lossless Codes With Generalized Criteria
- 2014
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 60:9, s. 5486-5499
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents lossless prefix codes optimized with respect to a payoff criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new coding algorithm, which transforms the initial source probability vector into a new probability vector according to a merging rule. The coding algorithm is equivalent to a partition of the source alphabet into disjoint sets on which a new transformed probability vector is defined as a function of the initial source probability vector and scalar parameter. The payoff criterion considered encompasses a tradeoff between maximum and average codeword length; it is related to a payoff criterion consisting of a convex combination of average codeword length and average of an exponential function of the codeword length, and to an average codeword length payoff criterion subject to a limited length constraint. A special case of the first related payoff is connected to coding problems involving source probability uncertainty and codeword overflow probability, whereas the second related payoff compliments limited length Huffman coding algorithms.
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| 6. |
- Stavrou, Photios A., et al.
(författare)
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Asymptotic Reverse-Waterfilling Characterization of Nonanticipative Rate Distortion Function of Vector-Valued Gauss-Markov Processes with MSE Distortion
- 2018
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Ingår i: 2018 IEEE Conference on Decision and Control (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781538613955 ; , s. 14-20
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Konferensbidrag (refereegranskat)abstract
- We analyze the asymptotic nonanticipative rate distortion function (NRDF) of vector-valued Gauss-Markov processes subject to a mean-squared error (MSE) distortion function. We derive a parametric characterization in terms of a reverse-waterfilling algorithm, that requires the solution of a matrix Riccati algebraic equation (RAE). Further, we develop an algorithm reminiscent of the classical reverse-waterfilling algorithm that provides an upper bound to the optimal solution of the reverse-waterfilling optimization problem, and under certain cases, it operates at the NRDF. Moreover, using the characterization of the reverse-waterfilling algorithm, we derive the analytical solution of the NRDF, for a simple two-dimensional parallel Gauss-Markov process. The efficacy of our proposed algorithm is demonstrated via an example.
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| 7. |
- Stavrou, Photios A., et al.
(författare)
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OPTIMAL ESTIMATION VIA NONANTICIPATIVE RATE DISTORTION FUNCTION AND APPLICATIONS TO TIME-VARYING GAUSS-MARKOV PROCESSES
- 2018
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Ingår i: SIAM Journal of Control and Optimization. - : SIAM PUBLICATIONS. - 0363-0129 .- 1095-7138. ; 56:5, s. 3731-3765
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we develop finite-time horizon causal filters for general processes taking values in Polish spaces using the nonanticipative rate distortion function (NRDF). Subsequently, we apply the NRDF to design optimal filters for time-varying vector-valued Gauss-Markov processes, subject to a mean-squared error (MSE) distortion. Unlike the classical Kalman filter design, the developed filters based on the NRDF are characterized parametrically by a dynamic reverse-waterfilling optimization problem obtained via Karush-Kuhn-Tucker conditions. We develop algorithms that provide, in general, tight upper bounds to the optimal solution to the dynamic reverse-waterfilling optimization problem subject to a total and per-letter MSE distortion constraint. Under certain conditions, these algorithms produce the optimal solutions. Further, we establish a universal lower bound on the total and per-letter MSE of any estimator of a Gaussian random process. Our theoretical framework is demonstrated via simple examples.
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| 8. |
- Tzortzis, Ioannis, et al.
(författare)
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Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics
- 2017
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Press. - 0018-9286 .- 1558-2523. ; 62:3, s. 1030-1045
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to approximate a Finite-State Markov (FSM) process by another process defined on a lower dimensional state space, called the approximating process, with respect to a total variation distance fidelity criterion. The approximation problem is formulated as an optimization problem using two different approaches. The first approach is based on approximating the transition probability matrix of the FSM process by a lower-dimensional transition probability matrix, resulting in an approximating process which is a Finite-State Hidden Markov (FSHM) process. The second approach is based on approximating the invariant probability vector of the original FSM process by another invariant probability vector defined on a lower-dimensional state space. Going a step further, a method is proposed based on optimizing a Kullback-Leibler divergence to approximate the FSHM processes by FSM processes. The solutions of these optimization problems are described by optimal partition functions which aggregate the states of the FSM process via a corresponding water-filling solution, resulting in lower-dimensional approximating processes which are FSHM or FSM processes. Throughout the paper, the theoretical results are justified by illustrative examples that demonstrate our proposed methodology.
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| 9. |
- Tzortzis, Ioannis, et al.
(författare)
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Dynamic programming subject to total variation distance ambiguity
- 2015
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 53:4, s. 2040-2075
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic control problem using minimax theory, in which the control minimizes the payoff while the conditional distribution, from the total variation distance set, maximizes it. First, we investigate the maximization of a linear functional on the space of probability measures on abstract spaces, among those probability measures which are within a total variation distance from a nominal probability measure, and then we give the maximizing probability measure in closed form. Second, we utilize the solution of the maximization to solve minimax stochastic control with deterministic control strategies, under a Markovian and a non-Markovian assumption, on the conditional distributions of the controlled process. The results of this part include (1) minimax optimization subject to total variation distance ambiguity constraint; (2) new dynamic programming recursions, which involve the oscillator seminorm of the value function, in addition to the standard terms; and (3) a new infinite horizon discounted dynamic programming equation, the associated contractive property, and a new policy iteration algorithm. Finally, we provide illustrative examples for both the finite and infinite horizon cases. For the infinite horizon case, we invoke the new policy iteration algorithm to compute the optimal strategies.
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| 10. |
- Stavrou, Photios A., et al.
(författare)
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Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
- 2018
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Ingår i: IEEE Journal on Selected Topics in Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1932-4553 .- 1941-0484. ; 12:5, s. 841-856
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Tidskriftsartikel (refereegranskat)abstract
- We deal with zero-delay source coding of a vector-valued Gauss-Markov source subject to a mean-squared error (MSE) fidelity criterion characterized by the operational zero-delay vector-valued Gaussian rate distortion function (RDF). We address this problem by considering the nonanticipative RDF (NRDF), which is a lower bound to the causal optimal performance theoretically attainable function (or simply causal RDF) and operational zero-delay RDF. We recall the realization that corresponds to the optimal "test-channel" of the Gaussian NRDF, when considering a vector Gauss-Markov source subject to a MSE distortion in the finite time horizon. Then, we introduce sufficient conditions to show existence of solution for this problem in the infinite time horizon (or asymptotic regime). For the asymptotic regime, we use the asymptotic characterization of the Gaussian NRDF to provide a new equivalent realization scheme with feedback, which is characterized by a resource allocation (reverse-waterfilling) problem across the dimension of the vector source. We leverage the new realization to derive a predictive coding scheme via lattice quantization with subtractive dither and joint memoryless entropy coding. This coding scheme offers an upper bound to the operational zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then for r active dimensions of the vector Gauss-Markov source the gap between the obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1 bits/vector. However, we further show that it is possible when we use vector quantization, and assume infinite dimensional Gauss-Markov sources to make the previous gap to be negligible, i.e., Gaussian NRDF approximates the operational zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian sources of any finite memory under mild conditions. Our theoretical framework is demonstrated with illustrative numerical experiments.
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