We introduce Pareto-NRPA, a new Monte-Carlo algorithm designed for multi-objective optimization problems over discrete search spaces. Extending the Nested Rollout Policy Adaptation (NRPA) algorithm originally formulated for single-objective problems, Pareto-NRPA generalizes the nested search and policy update mechanism to multi-objective optimization. The algorithm uses a set of policies to concurrently explore different regions of the solution space and maintains non-dominated fronts at each level of search. Policy adaptation is performed with respect to the diversity and isolation of sequences within the Pareto front. We benchmark Pareto-NRPA on two classes of problems: a novel bi-objective variant of the Traveling Salesman Problem with Time Windows problem (MO-TSPTW), and a neural architecture search task on well-known benchmarks. Results demonstrate that Pareto-NRPA achieves competitive performance against state-of-the-art multi-objective algorithms, both in terms of convergence and diversity of solutions. Particularly, Pareto-NRPA strongly outperforms state-of-the-art evolutionary multi-objective algorithms on constrained search spaces. To our knowledge, this work constitutes the first adaptation of NRPA to the multi-objective setting.

This paper addresses the problem of an aerial moving target search with a radar on an airborne platform.An observation of the radar is modeled as a cone covering a set of regions of the search area.We assume overlapping cones of observation, and we want to find the discrete allocation plan of search effort to the cones in order to optimize target detection.For the stationary target search with overlapping cones, we present a dynamic programming algorithm that computes the optimal allocation.An approximate greedy heuristic, which is more appropriate in a real time context, is also presented and assessed.The moving target search problem is solved with the Forward And Backward (FAB) algorithm coupled with the different stationary search algorithms.In this paper, we use a radar detection model that has been shown to be more realistic than the ones usually considered.Also, several models of movement of the target are considered with different Markovian transition matrices.We compare the performance of the mentioned algorithms on several scenarios.

This paper addresses the problem of a moving target search with a discrete allocation of search effort to disjoint cones of observation. A cone covers several regions with different visibilities. This is an important step towards the optimal search with radars on airborne platforms which has not been previously studied. We adapt Forward And Backward (FAB) algorithms to this problem and apply them to compute search plans. We measure the quality of our solution with a continuous relaxation of the problem. In a set of numerical experiments we exhibit that our algorithms have good performance in terms of plan quality and computation time. Finally, we compare the plans optimizing different objective functions.

Probabilistic Finite Automaton (PFA), Probabilistic Finite State Transducers (PFST) and Hidden Markov Models (HMM) are widely used in Automatic Speech Recognition (ASR), Text-to-Speech (TTS) systems and Part Of Speech (POS) tagging for language modeling. Traditionally, unsupervised learning of these latent variable models is done by Expectation-Maximization (EM)-like algorithms, as the Baum-Welch algorithm. In a recent alternative line of work, learning algorithms based on spectral properties of some low order moments matrices or tensors were proposed. In comparison to EM, they are orders of magnitude faster and come with theoretical convergence guarantees. However, returned models are not ensured to compute proper distributions. They often return negative values that do not sum to one, limiting their applicability and preventing them to serve as an initialization to EM-like algorithms. In this paper, we propose a new spectral algorithm able to learn a large range of models constrained to return proper distributions. We assess its performances on synthetic problems from the PAutomaC challenge and real datasets extracted from Wikipedia. Experiments show that it outperforms previous spectral approaches as well as the Baum-Welch algorithm with random restarts, in addition to serve as an efficient initialization step to EM-like algorithms.

This paper deals with a phase-coded waveform which combines two binary phase codes, each impacting on specific properties of the radar receiving channel. After giving a detailed analysis of the expression of the received signal after processing when the Gaussian clutter is modeled by a pth-order autoregressive process, we focus our attention on the choice of the two phase codes: one aims at increasing the unambiguous range whereas the other is chosen by taking into account several criteria such as the detection performance. For this purpose, we suggest determining the Pareto fronts of 1st, 2ndand 3rdorders by means of an exhaustive search. Given the three Pareto fronts for different types of clutters simulated by making the AR parameters vary, we provide an automatic way to determine, before embedding it, the most robust phase codes using a fuzzy logic operator.

Predictive State Representations (PSRs) are dynamical systems models that keep track of the system's state using predictions of future observations. In contrast to other models of dynamical systems, such as partially observable Markov decision processes, PSRs produces more compact models and can be consistently learned using statistics of the execution trace and spectral decomposition. In this paper we make a connection between rank minimization problems and learning PSRs. This allows us to derive a new algorithm based on nuclear norm minimization. In addition to estimate automatically the dimension of the system, our algorithm compares favorably with the state of art on randomly generated realistic problems of different sizes.

An original application of the weighted deflection is proposed for radar target classification by quadratic filters. An explicit formulation of optimal filters is derived. We analyse the impact of the weighting parameter on real data recognition, and show that performances are better when the deflection coincides with the Fisher ratio.