Related papers: Differentiable Game Mechanics
Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov chain on a general state space. Focusing on a class of…
We study infinite-horizon discounted two-player zero-sum Markov games, and develop a decentralized algorithm that provably converges to the set of Nash equilibria under self-play. Our algorithm is based on running an Optimistic Gradient…
Understanding the dynamics of optimization in deep learning is increasingly important as models scale. While stochastic gradient descent (SGD) and its variants reliably find solutions that generalize well, the mechanisms driving this…
In the last decade, deep learning has become a major component of artificial intelligence. The workhorse of deep learning is the optimization of loss functions by stochastic gradient descent (SGD). Traditionally in deep learning, neural…
Proximal gradient algorithms (PGA), while foundational for inverse problems like image reconstruction, often yield unstable convergence and suboptimal solutions by violating the critical non-negativity constraint. We identify the gradient…
Adversarial attacks can generate adversarial inputs by applying small but intentionally worst-case perturbations to samples from the dataset, which leads to even state-of-the-art deep neural networks outputting incorrect answers with high…
Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate…
Many applications in machine learning can be framed as minimization problems and solved efficiently using gradient-based techniques. However, recent applications of generative models, particularly GANs, have triggered interest in solving…
In this work, we present a learning-based nonlinear $H^\infty$ control algorithm that guarantee system performance under learned dynamics and disturbance estimate. The Gaussian Process (GP) regression is utilized to update the nominal…
The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically…
Prior work on differential privacy analysis of randomized SGD algorithms relies on composition theorems, where the implicit (unrealistic) assumption is that the internal state of the iterative algorithm is revealed to the adversary. As a…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
Dynamic difficulty adjustment ($DDA$) is a process of automatically changing a game difficulty for the optimization of user experience. It is a vital part of almost any modern game. Most existing DDA approaches concentrate on the experience…
The aim of decentralized gradient descent (DGD) is to minimize a sum of $n$ functions held by interconnected agents. We study the stability of DGD in open contexts where agents can join or leave the system, resulting each time in the…
Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This…
We study the convergence to local Nash equilibria of gradient methods for two-player zero-sum differentiable games. It is well-known that such dynamics converge locally when $S \succ 0$ and may diverge when $S=0$, where $S\succeq 0$ is the…
Most of the literature on learning in games has focused on the restrictive setting where the underlying repeated game does not change over time. Much less is known about the convergence of no-regret learning algorithms in dynamic multiagent…
We develop a game-theoretic framework for adversarially robust optimal safe predefined-time stabilization of parameter-dependent nonlinear dynamical systems with nonquadratic cost functionals. Our approach ensures that all system…