arXiv subjects

Yiguang Hong

Publications and source records attributed to Yiguang Hong.

At least 73 records · Page 4Linked to original sources

arXiv2022

A Survey of Decision Making in Adversarial Games

Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner, but without obvious malice to other players. However, in many practical applications, such as poker, chess, evader pursuing, drug interdiction, coast guard, cyber-security, and national defense, players often have apparently adversarial stances, that is, selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Along this line, this paper provides a systematic survey on three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

cs.GT↗

arXiv2022

Distributed Optimization with Projection-free Dynamics

We consider continuous-time dynamics for distributed optimization with set constraints in the paper. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with projection, we propose a distributed projection-free dynamics by employing the Frank-Wolfe method, also known as the conditional gradient algorithm. The process searches a feasible descent direction by solving an alternative linear optimization instead of a quadratic one. To make the approach applicable over weight-balanced digraphs, we design a dynamics for the consensus of local decision variables and another dynamics of auxiliary variables to track the global gradient. Then we prove the convergence of the dynamical systems to the optimal solution, and provide detailed numerical comparisons with both projection-based dynamics and other distributed projection-free algorithms. Also, we derive the distributed discrete-time scheme following the instructive ideas of the proposed dynamics and provide its accordingly convergence rate.

math.OC↗

arXiv2022

No-Regret Learning in Network Stochastic Zero-Sum Games

No-regret learning has been widely used to compute a Nash equilibrium in two-person zero-sum games. However, there is still a lack of regret analysis for network stochastic zero-sum games, where players competing in two subnetworks only have access to some local information, and the cost functions include uncertainty. Such a game model can be found in security games, when a group of inspectors work together to detect a group of evaders. In this paper, we propose a distributed stochastic mirror descent (D-SMD) method, and establish the regret bounds $O(\sqrt{T})$ and $O(\log T)$ in the expected sense for convex-concave and strongly convex-strongly concave costs, respectively. Our bounds match those of the best known first-order online optimization algorithms. We then prove the convergence of the time-averaged iterates of D-SMD to the set of Nash equilibria. Finally, we show that the actual iterates of D-SMD almost surely converge to the Nash equilibrium in the strictly convex-strictly concave setting.

math.OC↗

arXiv2022

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 algorithm, called Online Gradient Descent with lossy bandits (OGD-lb). We first give the regret analysis for concave games with differentiable and Lipschitz utilities. Then we show that the action profile converges to a Nash equilibrium with probability 1 when the game is also strictly monotone. We further provide the mean square convergence rate $\mathcal{O}\left(k^{-2\min\{β, 1/6\}}\right)$ when the game is $β-$ strongly monotone. In addition, we extend the algorithm to the case when the loss probability of the bandit feedback is unknown, and prove its almost sure convergence to Nash equilibrium for strictly monotone games. Finally, we take the resource management in fog computing as an application example, and carry out numerical experiments to empirically demonstrate the algorithm performance.

cs.LG↗

arXiv2022

Small-Gain Theorem for Safety Verification under High-Relative-Degree Constraints

This paper develops a small-gain technique for the safety analysis and verification of interconnected systems with high-relative-degree safety constraints. In this technique, input-to-state safety (ISSf) is used to characterize how the safety of a subsystem is influenced by the external input, and ISSf-barrier functions (ISSf-BFs) with high relative degree are employed to capture the safety of subsystems. With a coordination transform, the relationship between ISSf-BFs and the existing high-relative-degree (or high-order) barrier functions is established in order to simplify the ISSf analysis. With the help of high-relative-degree ISSf-BFs, a small-gain theorem is proposed for safety verification. It is shown that, under the small-gain condition, i) the interconnection of ISSf subsystems is still ISSf; and ii) the overall interconnected system is input-to-state stable (ISS) with respect to the compositional safe set. The effectiveness of the proposed small-gain theorem is illustrated on the output-constrained decentralized control of two inverted pendulums connected by a spring mounted on two carts.

eess.SY↗

arXiv2022

Distributed Variable Sample-size Stochastic Optimization with Fixed Step-sizes

The paper considers distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents' local expectation-valued convex cost functions. Due to the stochasticity in gradient observations, distributedness of local functions, and randomness of communication topologies, distributed algorithms with a convergence guarantee under fixed step-sizes have not been achieved yet. This work incorporates variance reduction scheme into the distributed stochastic gradient tracking algorithm, where local gradients are estimated by averaging across a variable number of sampled gradients. With an identically and independently distributed (i.i.d.) random network, we show that all agents' iterates converge almost surely to the same optimal solution under fixed step-sizes. When the global cost function is strongly convex and the sample size increases at a geometric rate, we prove that the iterates geometrically converge to the unique optimal solution, and establish the iteration, oracle, and communication complexity. The algorithm performance including rate and complexity analysis are further investigated with constant step-sizes and a polynomially increasing sample size. Finally, the empirical algorithm performance are illustrated with numerical examples.

math.OC↗

arXiv2022

Single-Leader-Multiple-Followers Stackelberg Security Game with Hypergame Framework

In this paper, we employ a hypergame framework to analyze the single-leader-multiple-followers (SLMF) Stackelberg security game with two typical misinformed situations: misperception and deception. We provide a stability criterion with the help of hyper Nash equilibrium (HNE) to investigate both strategic stability and cognitive stability of equilibria in SLMF games with misinformation. In fact, we find mild stable conditions such that the equilibria with misperception and deception can become HNE. Moreover, we discuss the robustness of the equilibria to reveal whether players have the ability to keep their profits under the influence of some misinformation.

cs.GT↗

arXiv2022

Multi-agent consensus over time-invariant and time-varying signed digraphs via eventual positivity

Laplacian dynamics on signed digraphs have a richer behavior than those on nonnegative digraphs. In particular, for the so-called "repelling" signed Laplacians, the marginal stability property (needed to achieve consensus) is not guaranteed a priori and, even when it holds, it does not automatically lead to consensus, as these signed Laplacians may loose rank even in strongly connected digraphs. Furthermore, in the time-varying case, instability can occur even when switching in a family of systems each of which corresponds to a marginally stable signed Laplacian with the correct corank. In this paper we present conditions guaranteeing consensus of these signed Laplacians based on the property of eventual positivity, a Perron-Frobenius type of property for signed matrices. The conditions cover both time-invariant and time-varying cases. A particularly simple sufficient condition valid in both cases is that the Laplacians are normal matrices. Such condition can be relaxed in several ways. For instance in the time-invariant case it is enough that the Laplacian has this Perron-Frobenius property on the right but not on the left side (i.e., on the transpose). For the time-varying case, convergence to consensus can be guaranteed by the existence of a common Lyapunov function for all the signed Laplacians. All conditions can be easily extended to bipartite consensus.

eess.SY↗

arXiv2021

Exponentially convergent distributed Nash equilibrium seeking for constrained aggregative games

Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is applicable to games with constrained strategy sets and weight-balanced communication graphs. We obtain an exponential convergence of the proposed algorithm to the Nash equilibrium. Numerical examples illustrate the effectiveness of our methods.

math.OC↗

arXiv2021

On Faster Convergence of Scaled Sign Gradient Descent

Communication has been seen as a significant bottleneck in industrial applications over large-scale networks. To alleviate the communication burden, sign-based optimization algorithms have gained popularity recently in both industrial and academic communities, which is shown to be closely related to adaptive gradient methods, such as Adam. Along this line, this paper investigates faster convergence for a variant of sign-based gradient descent, called scaled signGD, in three cases: 1) the objective function is strongly convex; 2) the objective function is nonconvex but satisfies the Polyak-Lojasiewicz (PL) inequality; 3) the gradient is stochastic, called scaled signGD in this case. For the first two cases, it can be shown that the scaled signGD converges at a linear rate. For case 3), the algorithm is shown to converge linearly to a neighborhood of the optimal value when a constant learning rate is employed, and the algorithm converges at a rate of $O(1/k)$ when using a diminishing learning rate, where $k$ is the iteration number. The results are also extended to the distributed setting by majority vote in a parameter-server framework. Finally, numerical experiments on logistic regression are performed to corroborate the theoretical findings.

math.OC↗

arXiv2021

Distributed Mirror Descent Algorithm with Bregman Damping for Nonsmooth Constrained Optimization

To solve distributed optimization efficiently with various constraints and nonsmooth functions, we propose a distributed mirror descent algorithm with embedded Bregman damping, as a generalization of conventional distributed projection-based algorithms. In fact, our continuous-time algorithm well inherits good capabilities of mirror descent approaches to rapidly compute explicit solutions to the problems with some specific constraint structures. Moreover, we rigorously prove the convergence of our algorithm, along with the boundedness of the trajectory and the accuracy of the solution.

math.OC↗

arXiv2021

Efficient algorithm for approximating Nash equilibrium of distributed aggregative games

In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such problems actually. Since it may be quite hard to get the exact projection in practice, we utilize inscribed polyhedrons to approximate local set constraints, which yields a related approximate game model. We first prove that the Nash equilibrium of the approximate game is the $ε$-Nash equilibrium of the original game, and then propose a distributed algorithm to seek the $ε$-Nash equilibrium, where the projection is then of a standard form in quadratic programming. With the help of the existing developed methods for solving quadratic programming, we show the convergence of the proposed algorithm, and also discuss the computational cost issue related to the approximation. Furthermore, based on the exponential convergence of the algorithm, we estimate the approximation accuracy related to $ε$. Additionally, we investigate the computational cost saved by approximation on numerical examples.

math.OC↗

arXiv2021

No-regret distributed learning in subnetwork zero-sum games

In this paper, we consider a distributed learning problem in a subnetwork zero-sum game, where agents are competing in different subnetworks. These agents are connected through time-varying graphs where each agent has its own cost function and can receive information from its neighbors. We propose a distributed mirror descent algorithm for computing a Nash equilibrium and establish a sublinear regret bound on the sequence of iterates when the graphs are uniformly strongly connected and the cost functions are convex-concave. Moreover, we prove its convergence with suitably selected diminishing stepsizes for a strictly convex-concave cost function. We also consider a constant step-size variant of the algorithm and establish an asymptotic error bound between the cost function values of running average actions and a Nash equilibrium. In addition, we apply the algorithm to compute a mixed-strategy Nash equilibrium in subnetwork zero-sum finite-strategy games, which have merely convex-concave (to be specific, multilinear) cost functions, and obtain a final-iteration convergence result and an ergodic convergence result, respectively, under different assumptions.

math.OC↗

arXiv2021

Composition and Application of Current Advanced Driving Assistance System: A Review

Due to the growing awareness of driving safety and the development of sophisticated technologies, advanced driving assistance system (ADAS) has been equipped in more and more vehicles with higher accuracy and lower price. The latest progress in this field has called for a review to sum up the conventional knowledge of ADAS, the state-of-the-art researches, and novel applications in real-world. With the help of this kind of review, newcomers in this field can get basic knowledge easier and other researchers may be inspired with potential future development possibility. This paper makes a general introduction about ADAS by analyzing its hardware support and computation algorithms. Different types of perception sensors are introduced from their interior feature classifications, installation positions, supporting ADAS functions, and pros and cons. The comparisons between different sensors are concluded and illustrated from their inherent characters and specific usages serving for each ADAS function. The current algorithms for ADAS functions are also collected and briefly presented in this paper from both traditional methods and novel ideas. Additionally, discussions about the definition of ADAS from different institutes are reviewed in this paper, and future approaches about ADAS in China are introduced in particular.

cs.AI↗

arXiv2021

Decentralized Online Learning for Noncooperative Games in Dynamic Environments

Decentralized online learning for seeking generalized Nash equilibrium (GNE) of noncooperative games in dynamic environments is studied in this paper. Each player aims at selfishly minimizing its own time-varying cost function subject to time-varying coupled constraints and local feasible set constraints. Only local cost functions and local constraints are available to individual players, who can receive their neighbors' information through a fixed and connected graph. In addition, players have no prior knowledge of cost functions and local constraint functions in the future time. In this setting, a novel distributed online learning algorithm for seeking GNE of the studied game is devised based on mirror descent and a primal-dual strategy. It is shown that the presented algorithm can achieve sublinearly bounded dynamic regrets and constraint violation by appropriately choosing decreasing stepsizes. Finally, the obtained theoretical result is corroborated by a numerical simulation.

math.OC↗

arXiv2021

Convergence Properties of the Distributed Projected Subgradient Algorithm over General Graphs

In this paper, we revisit a well-known distributed projected subgradient algorithm which aims to minimize a sum of cost functions with a common set constraint. In contrast to most of existing results, weight matrices of the time-varying multi-agent network are assumed to be more general, i.e., they are only required to be row stochastic instead of doubly stochastic. We focus on analyzing convergence properties of this algorithm under general graphs. We first show that there generally exists a graph sequence such that the algorithm is not convergent when the network switches freely within finitely many general graphs. Then to guarantee the convergence of this algorithm under any uniformly jointly strongly connected general graph sequence, we provide a necessary and sufficient condition, i.e., the intersection of optimal solution sets to all local optimization problems is not empty. Furthermore, we surprisingly find that the algorithm is convergent for any periodically switching general graph sequence, and the converged solution minimizes a weighted sum of local cost functions, where the weights depend on the Perron vectors of some product matrices of the underlying periodically switching graphs. Finally, we consider a slightly broader class of quasi-periodically switching graph sequences, and show that the algorithm is convergent for any quasi-periodic graph sequence if and only if the network switches between only two graphs.

math.OC↗

arXiv2021

Distributed Linear Equations over Random Networks

Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the equation via node-to-node communications, is a basic distributed computation task receiving an increasing research attention. Communications over a network have a stochastic nature, with both temporal and spatial dependence due to link failures, packet dropouts or node recreation, etc. In this paper, we study the convergence and convergence rate of distributed linear equation protocols over a $\ast$-mixing random network, where the temporal and spatial dependencies between the node-to-node communications are allowed. When the network linear equation admits exact solutions, we prove the mean-squared exponential convergence rate of the distributed projection consensus algorithm, while the lower and upper bound estimations of the convergence rate are also given for independent and identically distributed (i.i.d.) random graphs. Motivated by the randomized Kaczmarz algorithm, we also propose a distributed randomized projection consensus algorithm, where each node randomly selects one row of local linear equations for projection per iteration, and establish an exponential convergence rate. When the network linear equation admits no exact solution, we prove that a distributed gradient-descent-like algorithm with diminishing step-sizes can drive all nodes' states to a least-squares solution at a sublinear rate. These results collectively illustrate that distributed computations may overcome communication correlations if the prototype algorithms enjoy certain contractive properties or are designed with suitable parameters.

math.OC↗

arXiv2020

Small-Gain Theorem for Safety Verification of Interconnected Systems

A small-gain theorem in the formulation of barrier function is developed in this work for safety verification of interconnected systems. This result is helpful to verify input-to-state safety (ISSf) of the overall system from the safety information encoded in the subsystem's ISSf-barrier function. Also, it can be used to obtain a safety set in a higher dimensional space from the safety sets in two lower dimensional spaces.

eess.SY↗