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Register a new userSolving Large-Scale Extensive-Form Network Security Games via Neural Fictitious Self-Play
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Wanqi Xue
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Securing networked infrastructures is important in the real world. The problem of deploying security resources to protect against an attacker in networked domains can be modeled as Network Security Games (NSGs). Unfortunately, existing approaches, including the deep learning-based approaches, are inefficient to solve large-scale extensive-form NSGs. In this paper, we propose a novel learning paradigm, NSG-NFSP, to solve large-scale extensive-form NSGs based on Neural Fictitious Self-Play (NFSP). Our main contributions include: i) reforming the best response (BR) policy network in NFSP to be a mapping from action-state pair to action-value, to make the calculation of BR possible in NSGs; ii) converting the average policy network of an NFSP agent into a metric-based classifier, helping the agent to assign distributions only on legal actions rather than all actions; iii) enabling NFSP with high-level actions, which can benefit training efficiency and stability in NSGs; and iv) leveraging information contained in graphs of NSGs by learning efficient graph node embeddings. Our algorithm significantly outperforms state-of-the-art algorithms in both scalability and solution quality.
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The paper is concerned with distributed learning and optimization in large-scale settings. The well-known Fictitious Play (FP) algorithm has been shown to achieve Nash equilibrium learning in certain classes of multi-agent games. However, FP can be computationally difficult to implement when the number of players is large. Sampled FP is a variant of FP that mitigates the computational difficulties arising in FP by using a Monte-Carlo (i.e., sampling-based) approach. The Sampled FP algorithm has been studied both as a tool for distributed learning and as an optimization heuristic for large-scale problems. Despite its computational advantages, a shortcoming of Sampled FP is that the number of samples that must be drawn in each round of the algorithm grows without bound (on the order of $sqrt{t}$, where $t$ is the round of the repeated play). In this paper we propose Computationally Efficient Sampled FP (CESFP)---a variant of Sampled FP in which only one sample need be drawn each round of the algorithm (a substantial reduction from $O(sqrt{t})$ samples per round, as required in Sampled FP). CESFP operates using a stochastic-approximation type rule to estimate the expected utility from round to round. It is proven that the CESFP algorithm achieves Nash equilibrium learning in the same sense as classical FP and Sampled FP. Simulation results suggest that the convergence rate of CESFP (in terms of repeated-play iterations) is similar to that of Sampled FP.
Stochastic differential games have been used extensively to model agents competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets. The recently proposed machine learning algorithm, deep fictitious play, provides a novel efficient tool for finding Markovian Nash equilibrium of large $N$-player asymmetric stochastic differential games [J. Han and R. Hu, Mathematical and Scientific Machine Learning Conference, pages 221-245, PMLR, 2020]. By incorporating the idea of fictitious play, the algorithm decouples the game into $N$ sub-optimization problems, and identifies each players optimal strategy with the deep backward stochastic differential equation (BSDE) method parallelly and repeatedly. In this paper, we prove the convergence of deep fictitious play (DFP) to the true Nash equilibrium. We can also show that the strategy based on DFP forms an $eps$-Nash equilibrium. We generalize the algorithm by proposing a new approach to decouple the games, and present numerical results of large population games showing the empirical convergence of the algorithm beyond the technical assumptions in the theorems.
We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary. We define three different scenarios according to the communication capabilities of the team. In the first, the teammates can communicate and correlate their actions both before and during the play. In the second, they can only communicate before the play. In the third, no communication is possible at all. We define the most suitable solution concepts, and we study the inefficiency caused by partial or null communication, showing that the inefficiency can be arbitrarily large in the size of the game tree. Furthermore, we study the computational complexity of the equilibrium-finding problem in the three scenarios mentioned above, and we provide, for each of the three scenarios, an exact algorithm. Finally, we empirically evaluate the scalability of the algorithms in random games and the inefficiency caused by partial or null communication.
Optimization of deep learning algorithms to approach Nash Equilibrium remains a significant problem in imperfect information games, e.g. StarCraft and poker. Neural Fictitious Self-Play (NFSP) has provided an effective way to learn approximate Nash Equilibrium without prior domain knowledge in imperfect information games. However, optimality gap was left as an optimization problem of NFSP and by solving the problem, the performance of NFSP could be improved. In this study, focusing on the optimality gap of NFSP, we have proposed a new method replacing NFSPs best response computation with regret matching method. The new algorithm can make the optimality gap converge to zero as it iterates, thus converge faster than original NFSP. We have conduct experiments on three typical environments of perfect-information games and imperfect information games in OpenSpiel and all showed that our new algorithm performances better than original NFSP.
One practical requirement in solving dynamic games is to ensure that the players play well from any decision point onward. To satisfy this requirement, existing efforts focus on equilibrium refinement, but the scalability and applicability of existing techniques are limited. In this paper, we propose Temporal-Induced Self-Play (TISP), a novel reinforcement learning-based framework to find strategies with decent performances from any decision point onward. TISP uses belief-space representation, backward induction, policy learning, and non-parametric approximation. Building upon TISP, we design a policy-gradient-based algorithm TISP-PG. We prove that TISP-based algorithms can find approximate Perfect Bayesian Equilibrium in zero-sum one-sided stochastic Bayesian games with finite horizon. We test TISP-based algorithms in various games, including finitely repeated security games and a grid-world game. The results show that TISP-PG is more scalable than existing mathematical programming-based methods and significantly outperforms other learning-based methods.
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