Related papers: On the Properties of the Softmax Function with App…
We investigate the convergence rates of the trajectories generated by implicit first and second order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz…
Reinforcement learning (RL) agents can leverage batches of previously collected data to extract a reasonable control policy. An emerging issue in this offline RL setting, however, is that the bootstrapping update underlying many of our…
We address learning Nash equilibria in convex games under the payoff information setting. We consider the case in which the game pseudo-gradient is monotone but not necessarily strictly monotone. This relaxation of strict monotonicity…
Latent categorical variables are frequently found in deep learning architectures. They can model actions in discrete reinforcement-learning environments, represent categories in latent-variable models, or express relations in graph neural…
Two main families of reinforcement learning algorithms, Q-learning and policy gradients, have recently been proven to be equivalent when using a softmax relaxation on one part, and an entropic regularization on the other. We relate this…
This paper proposes a novel fuzzy action selection method to leverage human knowledge in reinforcement learning problems. Based on the estimates of the most current action-state values, the proposed fuzzy nonlinear mapping as-signs each…
In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately,…
Smooth game optimization has recently attracted great interest in machine learning as it generalizes the single-objective optimization paradigm. However, game dynamics is more complex due to the interaction between different players and is…
In the past few years, Softmax has become a common component in neural network frameworks. In this paper, a gradient decay hyperparameter is introduced in Softmax to control the probability-dependent gradient decay rate during training. By…
Softmax function is widely used in artificial neural networks for multiclass classification, multilabel classification, attention mechanisms, etc. However, its efficacy is often questioned in literature. The log-softmax loss has been shown…
Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…
We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations,…
We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a…
Value function estimation is an important task in reinforcement learning, i.e., prediction. The Boltzmann softmax operator is a natural value estimator and can provide several benefits. However, it does not satisfy the non-expansion…
In this paper, we address the problem of interpolation of smooth convex-concave functions. Interpolation is a key step for computer-assisted estimation of worst-case performance via PEP-like techniques, and smooth convex-concave functions…
In recent years, the softmax model and its fast approximations have become the de-facto loss functions for deep neural networks when dealing with multi-class prediction. This loss has been extended to language modeling and recommendation,…
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such…
Deep neural networks are vulnerable to adversarial attacks. Recent studies about adversarial robustness focus on the loss landscape in the parameter space since it is related to optimization and generalization performance. These studies…
This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Same properties for the ratio of the modified Lommel functions with the Lommel function,…
In decision-dependent games, multiple players optimize their decisions under a data distribution that shifts with their joint actions, creating complex dynamics in applications like market pricing. A practical consequence of these dynamics…