单调凹博弈中的连续时间折扣镜像下降动力学

目标镜像下降：一种求解单调变分不等式的统一框架

Target Mirror Descent: A Unifying Framework for Solving Monotone Variational Inequalities

本文提出目标镜像下降框架，通过双变量修正机制稳定单调流，统一了近端点算法、extragradient方法等经典算法，并改进了折扣镜像下降的均衡偏差。

强单调与指数凹博弈中基于梯度反馈的自适应双重最优无悔学习

Adaptive, Doubly Optimal No-Regret Learning in Strongly Monotone and Exp-Concave Games with Gradient Feedback

本文提出无需预知强凸/强单调参数的自适应算法AdaOGD，在单智能体强凸优化和强单调博弈中分别实现接近最优的遗憾界与最终迭代收敛速率，并首次为报童问题提供可行且接近最优的学习算法。

Tensor methods for strongly convex strongly concave saddle point problems and strongly monotone variational inequalities

In this paper we propose three $p$-th order tensor methods for $μ$-strongly-convex-strongly-concave saddle point problems (SPP). The first method is based on the assumption of $p$-th order smoothness of the objective and it achieves a convergence rate of $O \left( \left( \frac{L_p R^{p - 1}}μ \right)^\frac{2}{p + 1} \log \frac{μR^2}{\varepsilon_G} \right)$, where $R$ is an estimate of the initial distance to the solution, and $\varepsilon_G$ is the error in terms of duality gap. Under additional assumptions of first and second order smoothness of the objective we connect the first method with …

关于马尔可夫说服价值的单调性和收敛速率

On the Monotonicity and Rate of Convergence of the Markovian Persuasion Value

本文研究了马尔可夫说服模型中说服价值的单调性和收敛速率，推导了δ-折扣价值随δ趋近于1时的收敛速率上界，并将其扩展到马尔可夫链博弈模型。

超越一阶方法的非凸非凹极小极大优化

Beyond first-order methods for non-convex non-concave min-max optimization

本文研究非凸非凹极小极大优化问题，提出超越一阶方法的高阶方法，在弱化Minty条件下建立O(1/ε^(2/p))速率，并验证其优于一阶方法。

凸非严格单调博弈中的 Bandit 学习

Bandit Learning in Convex Non-Strictly Monotone Games

针对伪梯度仅单调的凸博弈，提出一种可收敛至最小范数 Nash 均衡的 Bandit 学习算法，并基于在线优化视角分析遗憾率及参数选择。

Generalized Mirror Prox for Monotone Variational Inequalities: Universality and Inexact Oracle

We introduce an inexact oracle model for variational inequalities (VI) with monotone operator, propose a numerical method which solves such VI's and analyze its convergence rate. As a particular case, we consider VI's with Hölder-continuous operator and show that our algorithm is universal. This means that without knowing the Hölder parameter $ν$ and Hölder constant $L_ν$ it has the best possible complexity for this class of VI's, namely our algorithm has complexity $O\left( \inf_{ν\in[0,1]}\left(\frac{L_ν}{\varepsilon} \right)^{\frac{2}{1+ν}}R^2 \right)$, where $R$ is the size of the feasible…

Optimal Algorithms for Continuous Non-monotone Submodular and DR-Submodular Maximization

In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications in machine learning, economics, and communication systems. Our main result is the first $\frac{1}{2}$-approximation algorithm for continuous submodular function maximization; this approximation factor of $\frac{1}{2}$ is the best possible for algorithms that only query the objective function at polynomially many points. For the special case of DR-submodular m…

具有受控波动率的位移单调平均场博弈的定量收敛

Quantitative convergence for displacement monotone mean field games with controlled volatility

研究具有共同噪声和受控波动率的平均场博弈收敛问题，通过最大值原理将其转化为前向-后向混沌传播问题，并利用位移单调性首次为共同噪声受控博弈提供了开环Nash均衡的定量收敛证明。

Tight Last-Iterate Convergence of the Extragradient and the Optimistic Gradient Descent-Ascent Algorithm for Constrained Monotone Variational Inequalities

The monotone variational inequality is a central problem in mathematical programming that unifies and generalizes many important settings such as smooth convex optimization, two-player zero-sum games, convex-concave saddle point problems, etc. The extragradient algorithm by Korpelevich [1976] and the optimistic gradient descent-ascent algorithm by Popov [1980] are arguably the two most classical and popular methods for solving monotone variational inequalities. Despite their long histories, the following major problem remains open. What is the last-iterate convergence rate of the extragradient…

锚定梯度下降的最后迭代收敛性

Last-Iterate Convergence of Anchored Gradient Descent

本文研究了单调包含问题，提出扩展锚定梯度下降方法并证明了其在切线残差下的O(1/√T)收敛率。

强单调博弈中带赌博机反馈的双重最优无悔在线学习

Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedback

本文针对强单调博弈中的赌博机反馈在线学习问题，提出基于自协调障碍函数的新算法，首次同时实现单智能体最优遗憾和多智能体最优末次迭代收敛速率，解决了该领域长期存在的开放问题。

No-regret learning for repeated non-cooperative games with lossy bandits

This paper considers no-regret learning for repeated continuous-kernel games with lossy bandit feedback. Since it is difficult to give the explicit model of the utility functions in dynamic environments, the players' action can only be learned with bandit feedback. Moreover, because of unreliable communication channels or privacy protection, the bandit feedback may be lost or dropped at random. Therefore, we study the asynchronous online learning strategy of the players to adaptively adjust the next actions for minimizing the long-term regret loss. The paper provides a novel no-regret learning…