## 1 Introduction
The authors of [12] also considered the partial observable problem of the multi-armed bandit (MAB) with side observation, and modeled it as a graph structure to describe regret according to the dominance and independence numbers of the observability graph. Based on the above literature survey, we conclude that the multi-channel power allocation problem under a one-shot confrontation scenario with the communication capacity as the optimization objective has been solved well. However, the multi-channel power allocation problem, which takes the number of successfully transmitted channels as the optimization objective, needs to be further studied, and the solution method needs to be further optimized. Therefore, we study the multi-channel power allocation problem based on the BG model with the number of successful transmission channels as the optimization objective, and improve the model solving method to avoid the dilemma of finding a specific Nash equilibrium determined by the joint probability distribution function. For the multi-channel power allocation problem under a repeated confrontation scenario, we are inspired by the online learning problem under the partially observable model and transform the multi-channel power allocation problem under a repeated confrontation scenario into a graph structure problem, and the objective of model solving is to minimize the expected regret of the communication parties after multiple confrontation. It should be noted that each round of interaction in the repeated confrontations is modeled based on the BG model. A generalized BG is a two-player zero-sum game for competitive resource allocation. Each player has a fixed resource budget and simultaneously allocates their resources to \(n\) battlefields. When a participant allocates more resources than the opponent on a certain battlefield, they will gain the battlefield, and the corresponding side that wins more battlefields is the final winner [13]. Although the rules of the game are very simple, the number of potential battlefields and the total resources of each player can vary, so the potential strategies that players can employ are almost limitless. These two kinds of confrontation scenario proposed in this paper can be constructed on the basis of the Blotto Game model, and the models under different problems can be solved respectively. The main work and contributions of this paper are as follows:  
* First, for the problem of multi-channel power allocation under a one-shot confrontation scenario, we model the problem based on the BG model. We also design the DO-SINR (Double Oracle-Signal-to-Interference-plus-Noise Ratio) algorithm with the number of channels as the optimization objective to solve the approximate Nash equilibrium of the game between the two parties, avoiding the dilemma of finding the specific Nash equilibrium determined by the joint probability distribution function. The result can be used in the case of online games, if the jammer adopts an approximate Nash equilibrium, and the communication parties have no prior knowledge of the opponent, then the approximate Nash equilibrium strategy is an optional strategy;
* Second, we study the problem of multi-channel power allocation under a repeated confrontation scenario. We transform the problem into a shortest path problem with a graph structure to make the problem-solving process more intuitive, and then design the Exp3-U (Exp3-Uniform) algorithm based on the graph structure to solve the resource allocation problem under the condition of repeated games. Experiments show the effectiveness of our algorithm in minimizing the expected regret of communication parties during online confrontation while maintaining good operating efficiency. In these two works, the problem of multi-channel power allocation under a one-shot confrontation scenario can be regarded as offline setting, and the approximate Nash equilibrium of the problem can be used as a blueprint strategy for online setting.