随机微分博弈与带跳随机偏微分方程及人工智能AlphaGo
- 论文题目
- 英文摘要
We establish a relationship between stochastic differential games (SDGs) and a unified forward-backward coupled stochastic partial
differential equation (SPDE) with discontinuous Levy Jumps. The SDGs have q players and are driven by a general-dimensional
vector Levy process. By establishing a vector-form Ito-Ventzell's formula and a 4-tuple vector-field solution to the unified SPDE,
we get a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum
sense. The unified SPDE is in both general dimensional vector-form and forward-backward coupling manner. The partial differential
operators in its drift, diffusion, and jump coefficients are in time-variable and position-parameters over a domain. Since the
unified SPDE is of general nonlinearity and general high-order, we extend our recent study from the existing Brownian motion (BM)
driven backward case to a general Levy driven forward-backward coupled case. In doing so, we construct a new topological space to
support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense.
The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents
{gamma_{1},gamma_{2},...} under a set of general localized conditions, which is significantly different from the construction of
the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Levy
jumps, our study is also significantly different from the BM driven backward case. The coupling between forward and backward SPDEs
essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model
for generative AI.
- 中文介绍
- 关键词与关键技术
- Stochastic differential game, non-zero-sum game, zero-sum game, non-Gaussian noise, stochastic partial differential equation,
discontinuous Levy jump, forward and backward coupling, diffusion transformer.
- 该文被选为杂志封面介绍论文(This paper is selected to be introduced on the journal cover)
- Cover Story (in the following journal cover): In the upper graph, the admission control for inputs in an access network may correspond to a zero-sum game policy.
The routing balance between two nodes may correspond to a non-zero-sum game policy, where p is a trainable routing probability. These
game-theoretic policies may be obtained through the solution of a unified stochastic partial differential equation (SPDE) with Levy
discontinuous jumps. In the lower graph, two sample surfaces are drawn for the solution of the SPDE.
- AlphaGo名词解释与相关国际会议
- “AlphaGo”通常翻译成“阿尔法狗”，是美国谷歌(Google)公司基于围棋发明的一种人工智能系统，也可以说是一个机器人，成功战胜了世界围棋冠军。
它的进一步发展被称为是"AlphaFold"，可用来预测基因蛋白质结构并用来发展有效药物治疗疾病。“AlphaGo”与经济学中的Alpha策略(Alpha Policy)
相对应，意指最好策略。与此相关，我们文中首次用带跳随机微分方程与博弈论的方法发展了AlphaGo的终极博弈输赢动力系统模型，在前期的国际大会
主旨报告中，我们称相应的决策为”BestGo"，与“阿尔法狗”相对应，我们称其为“百思狗”。
- 相关论文
- 点击这里查看更多相关论文
|
