TSOM: Small Object Motion Detection Neural Network Inspired by Avian Visual Circuit

Detecting small moving objects in complex backgrounds from an overhead perspective is a highly challenging task for machine vision systems. As an inspiration from nature, the avian visual system is capable of processing motion information in various complex aerial scenes, and its Retina-OT-Rt visual circuit is highly sensitive to capturing the motion information of small objects from high altitudes. However, more needs to be done on small object motion detection algorithms based on the avian visual system. In this paper, we conducted mathematical modeling based on extensive studies of the biological mechanisms of the Retina-OT-Rt visual circuit. Based on this, we proposed a novel tectum small object motion detection neural network (TSOM). The neural network includes the retina, SGC dendritic, SGC Soma, and Rt layers, each layer corresponding to neurons in the visual pathway. The Retina layer is responsible for accurately projecting input content, the SGC dendritic layer perceives and encodes spatial-temporal information, the SGC Soma layer computes complex motion information and extracts small objects, and the Rt layer integrates and decodes motion information from multiple directions to determine the position of small objects. Extensive experiments on pigeon neurophysiological experiments and image sequence data showed that the TSOM is biologically interpretable and effective in extracting reliable small object motion features from complex high-altitude backgrounds.

A Large Deviations Perspective on Policy Gradient Algorithms

We derive the first large deviation rate function for the stochastic iterates generated by policy gradient methods with a softmax parametrization and an entropy regularized objective. Leveraging the contraction principle from large deviations theory, we also develop a general recipe for deriving exponential convergence rates for a wide spectrum of other policy parametrizations. This approach unifies several results from the literature and simplifies existing proof techniques.

Policy Gradient Algorithms for Robust MDPs with Non-Rectangular Uncertainty Sets

We propose a policy gradient algorithm for robust infinite-horizon Markov Decision Processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that display statistical optimality properties and make optimal use of limited data often fail to be rectangular. Unfortunately, the corresponding robust MDPs cannot be solved with dynamic programming techniques and are in fact provably intractable. This prompts us to develop a projected Langevin dynamics algorithm tailored to the robust policy evaluation problem, which offers global optimality guarantees. We also propose a deterministic policy gradient method that solves the robust policy evaluation problem approximately, and we prove that the approximation error scales with a new measure of non-rectangularity of the uncertainty set. Numerical experiments showcase that our projected Langevin dynamics algorithm can escape local optima, while algorithms tailored to rectangular uncertainty fail to do so.

Distributionally Robust Optimization with Markovian Data

We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We propose a data-driven distributionally robust optimization model to estimate the problem's objective function and optimal solution. By leveraging results from large deviations theory, we derive statistical guarantees on the quality of these estimators. The underlying worst-case expectation problem is nonconvex and involves $\mathcal O(d^2)$ decision variables. Thus, it cannot be solved efficiently for large $d$. By exploiting the structure of this problem, we devise a customized Frank-Wolfe algorithm with convex direction-finding subproblems of size $\mathcal O(d)$. We prove that this algorithm finds a stationary point efficiently under mild conditions. The efficiency of the method is predicated on a dimensionality reduction enabled by a dual reformulation. Numerical experiments indicate that our approach has better computational and statistical properties than the state-of-the-art methods.