We study pure exploration in multi armed bandits with graph side information. In particular, we consider the best-arm and near best-arm identification problem in the fixed confidence setting under the assumption that the arm rewards are smooth with respect to a given arbitrary graph. This captures a range of real world pure exploration scenarios where one often has information about the similarity of the options or actions under consideration. We propose a novel algorithm GRUB for this problem and provide a theoretical characterization of its performance that elicits the benefit of the graph side information. We complement our theory with experimental results that show that capitalizing on available graph side information yields significant improvements over pure exploration methods that are unable to use this information

Hyperspectral unmixing is an important remote sensing task with applications including material identification and analysis. Characteristic spectral features make many pure materials identifiable from their visible-to-infrared spectra, but quantifying their presence within a mixture is a challenging task due to nonlinearities and factors of variation. In this paper, spectral variation is considered from a physics-based approach and incorporated into an end-to-end spectral unmixing algorithm via differentiable programming. The dispersion model is introduced to simulate realistic spectral variation, and an efficient method to fit the parameters is presented. Then, this dispersion model is utilized as a generative model within an analysis-by-synthesis spectral unmixing algorithm. Further, a technique for inverse rendering using a convolutional neural network to predict parameters of the generative model is introduced to enhance performance and speed when training data is available.

We consider the problem of recovering a complex vector from m quadratic measurements. This problem, known as quadratic feasibility, encompasses the well known phase retrieval problem and has applications in a wide range of important areas including power system state estimation and x-ray crystallography. In general, not only is the the quadratic feasibility problem NP-hard to solve, but it may in fact be unidentifiable. In this paper, we establish conditions under which this problem becomes identifiable, and further prove isometry properties in the case when the matrices are Hermitian matrices sampled from a complex Gaussian distribution. Moreover, we explore a nonconvex optimization formulation of this problem, and establish salient features of the associated optimization landscape that enables gradient algorithms with an arbitrary initialization to converge to a globally optimal point with a high probability. Our results also reveal sample complexity requirements for successfully identifying a feasible solution in these contexts.

We study the problem of minimization of loss function $f(X)$ over the set of all $n$ x $m$ matrices $X$ of rank $r$. We propose a bi-level extention to Factored Gradient descent (FGD) algorithm and show its theoretical convergence and simulation results. On a side note, we also suggest methods of reducing computation complexity of projection based algorithms by cutting down on the number of projection operation in a standard constrained optimization approach. We also analyse the benefits and limitations of this approach.

Motivated by applications in competitive WiFi sensing, and competition to grab user attention in social networks, the problem of when to arrive at/sample a shared resource/server platform with multiple players is considered. Server activity is intermittent, with the server switching between between ON and OFF periods alternatively. Each player spends a certain cost to sample the server state, and due of competition, the per-player service rate is inversely proportional to the number of connected/ arrived players. The objective of each player is to arrive/ sample the server as soon as any ON period begins while incurring minimal sensing cost and to avoid having many other players overlap in time with itself. For this competition model, we propose a distributed randomized learning algorithm (strategy to sample the server) for each player, which is shown to converge to a unique non-trivial fixed point. The fixed point is moreover shown to be a Nash equilibrium of a sensing game, where each player’s utility function is demonstrated to possess all the required selfishness tradeoffs