Related papers: DPER: Dynamic Programming for Exist-Random Stochas…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal…
The determinantal point process (DPP) is an elegant probabilistic model of repulsion with applications in various machine learning tasks including summarization and search. However, the maximum a posteriori (MAP) inference for DPP which…
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use…
We develop a framework for obtaining polynomial time approximation schemes (PTAS) for a class of stochastic dynamic programs. Using our framework, we obtain the first PTAS for the following stochastic combinatorial optimization problems:…
We consider the problem of upper bounding the expected log-likelihood sub-optimality of the maximum likelihood estimate (MLE), or a conjugate maximum a posteriori (MAP) for an exponential family, in a non-asymptotic way. Surprisingly, we…
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…
A reliable support detection is essential for a greedy algorithm to reconstruct a sparse signal accurately from compressed and noisy measurements. This paper proposes a novel support detection method for greedy algorithms, which is referred…
We design a new myopic strategy for a wide class of sequential design of experiment (DOE) problems, where the goal is to collect data in order to to fulfil a certain problem specific goal. Our approach, Myopic Posterior Sampling (MPS), is…
Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution…
A wide variety of phenomena of engineering and scientific interest are of a continuous-time nature and can be modeled by stochastic differential equations (SDEs), which represent the evolution of the uncertainty in the states of a system.…
Answer Set Programming (ASP) provides a powerful declarative paradigm for knowledge representation and reasoning. Recently, counting answer sets has emerged as an important computational problem with applications in probabilistic reasoning,…
This paper studies the maximum cardinality matching problem in stochastically evolving graphs. We formally define the arrival-departure model with stochastic departures. There, a graph is sampled from a specific probability distribution and…
It is well-know that deciding consistency for normal answer set programs (ASP) is NP-complete, thus, as hard as the satisfaction problem for classical propositional logic (SAT). The best algorithms to solve these problems take exponential…
In this paper, we study the Dynamic Parameterized Subset Sampling (DPSS) problem in the Word RAM model. In DPSS, the input is a set,~$S$, of~$n$ items, where each item,~$x$, has a non-negative integer weight,~$w(x)$. Given a pair of query…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
In this paper, we propose novel algorithms for inferring the Maximum a Posteriori (MAP) solution of discrete pairwise random field models under multiple constraints. We show how this constrained discrete optimization problem can be…
We consider a class of sparsity-inducing optimization problems whose constraint set is regularizer-compatible, in the sense that, the constraint set becomes easy-to-project-onto after a coordinate transformation induced by the…
In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the…
Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for…