Related papers: On the Properties of the Softmax Function with App…

We introduce a temperature into the exponential function and replace the softmax output layer of neural nets by a high temperature generalization. Similarly, the logarithm in the log loss we use for training is replaced by a low temperature…

In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal…

The popular softmax loss and its recent extensions have achieved great success in the deep learning-based image classification. However, the data for training image classifiers usually has different quality. Ignoring such problem, the…

We illustrate the detrimental effect, such as overconfident decisions, that exponential behavior can have in methods like classical LDA and logistic regression. We then show how polynomiality can remedy the situation. This, among others,…

In this paper, we propose a passivity-based methodology for analysis and design of reinforcement learning in multi-agent finite games. Starting from a known exponentially-discounted reinforcement learning scheme, we show that convergence to…

SoftMax is a ubiquitous ingredient of modern machine learning algorithms. It maps an input vector onto a probability simplex and reweights the input by concentrating the probability mass at large entries. Yet, as a smooth approximation to…

In reinforcement learning, the softmax parametrization is the standard approach for policies over discrete action spaces. However, it fails to capture the order relationship between actions. Motivated by a real-world industrial problem, we…

Deep learning has non-convex loss landscape and its optimization dynamics is hard to analyze or control. Nevertheless, the dynamics can be empirically convex-like across various tasks, models, optimizers, hyperparameters, etc. In this work,…

In a multirobot system, a number of cyber-physical attacks (e.g., communication hijack, observation perturbations) can challenge the robustness of agents. This robustness issue worsens in multiagent reinforcement learning because there…

We mainly establish a monotonicity property between some special Riemann sums of a convex function $f$ on $[a,b]$, which in particular yields that $\frac{b-a}{n+1}\sum_{i=0}^n f\left(a+i\frac{b-a}{n}\right)$ is decreasing while…

In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…

We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and…

In this paper, we approach the problem of finding the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space via an implicit forward-backward-forward dynamical system with…

We study the transfer of rewards learned using inverse reinforcement learning from expert demonstrations in one environment to reinforcement learning in a new, different environment. This arises naturally when demonstrations are collected…

Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…

This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis,…

In Learning Theory, the smoothness assumption on the target function (known as source condition) is a key factor in establishing theoretical convergence rates for an estimator. The existing general form of the source condition, as discussed…

The $Q$-function is a central quantity in many Reinforcement Learning (RL) algorithms for which RL agents behave following a (soft)-greedy policy w.r.t. to $Q$. It is a powerful tool that allows action selection without a model of the…

Projected policy gradient under the simplex parameterization, policy gradient and natural policy gradient under the softmax parameterization, are fundamental algorithms in reinforcement learning. There have been a flurry of recent…

We perform the first tight convergence analysis of the gradient method with varying step sizes when applied to smooth hypoconvex (weakly convex) functions. Hypoconvex functions are smooth nonconvex functions whose curvature is bounded and…