Related papers: On the Properties of the Softmax Function with App…
The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
We study differentiability properties of convex operators defined on a Banach space with values in an $\Lc_p$ space and of their compositions with monotonic convex functionals on this space. We develop new tools for operators enjoying an…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems…
Researchers are increasingly focusing on intelligent games as a hot research area.The article proposes an algorithm that combines the multi-attribute management and reinforcement learning methods, and that combined their effect on…
In the present paper, the following convexity principle is proved: any closed convex multifunction, which is metrically regular in a certain uniform sense near a given point, carries small balls centered at that point to convex sets, even…
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…
Typically, Softmax is used in the final layer of a neural network to get a probability distribution for output classes. But the main problem with Softmax is that it is computationally expensive for large scale data sets with large number of…
Deep networks have enabled reinforcement learning to scale to more complex and challenging domains, but these methods typically require large quantities of training data. An alternative is to use sample-efficient episodic control methods:…
The monotonicity of the Mittag-Leffler function $E_{\alpha}$ with respect to the parameter $\alpha$ is investigated, via some convex ordering properties for related random variables. In particular, it is shown that the mapping…
Exploration-exploitation dilemma has long been a crucial issue in reinforcement learning. In this paper, we propose a new approach to automatically balance between these two. Our method is built upon the Soft Actor-Critic (SAC) algorithm,…
The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…
This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
In this paper, we address the inverse problem for linear-quadratic differential non-cooperative games with output-feedback. Given players' stabilizing feedback laws, the goal is to find cost function parameters that lead to a game for which…
We consider the inverse problem of dynamic games, where cost function parameters are sought which explain observed behavior of interacting players. Maximum entropy inverse reinforcement learning is extended to the N-player case in order to…
We show that the thermal subadditivity of entropy provides a common basis to derive a strong form of the bounded difference inequality and related results as well as more recent inequalities applicable to convex Lipschitz functions, random…
Penalty functions are widely used to enforce constraints in optimization problems and reinforcement leaning algorithms. Softplus and algebraic penalty functions are proposed to overcome the sensitivity of the Courant-Beltrami method to…
Numerous models for supervised and reinforcement learning benefit from combinations of discrete and continuous model components. End-to-end learnable discrete-continuous models are compositional, tend to generalize better, and are more…