Maneuverable threat poses significant risks to the operational safety of spacecraft in orbit, thereby jeopardizing mission success in the contested space environment. To address the coordinated orbital game between multiple pursuers (spacecraft) and one evader (threat), this paper proposes a reward-centering multi-agent deep deterministic policy gradient (MADDPG) algorithm, which has two-folds: Firstly, a relative dynamical model consideringJ2perturbation is established to characterize orbital interactions among multiple players, laying a physics-based foundation for decision-making. Secondly, an improved multi-agent reinforcement learning framework is constructed with two components. For individual spacecraft of multiple pursuers, a state-driven exploration-exploitation tradeoff mechanism is incorporated to avoid suboptimal strategy convergence. For the spacecraft group (namely multiple pursuers), reward functions are designed to align individual behaviors with collective objectives. Furthermore, a reward-centering mechanism along with theoretical analysis is introduced to dynamically calibrate the reward baseline, which stabilizes policy update via reducing gradient variance. Simulation results show the proposed algorithm enables spacecraft to autonomously develop coordinated strategies, ultimately confining the threat within predefined interception threshold.

This paper considers a canonical problem in kernel regression: how good are the model performances when it is trained by the popular online first-order algorithms, compared to the offline ones, such as ridge and ridgeless regression? In this paper, we analyze the foundational single-pass Stochastic Gradient Descent (SGD) in kernel regression under source condition where the optimal predictor can even not belong to the RKHS, i.e. the model is misspecified. Specifically, we focus on the inner product kernel over the sphere and characterize the exact orders of the excess risk curves under different scales of sample sizes $n$ concerning the input dimension $d$. Surprisingly, we show that SGD achieves min-max optimal rates up to constants among all the scales, $without$ suffering the saturation, a prevalent phenomenon observed in (ridge) regression, except when the model is highly misspecified and the learning is in a final stage where $n\gg d^\gamma$ with any constant $\gamma >0$. The main reason for SGD to overcome the curse of saturation is the exponentially decaying step size schedule, a common practice in deep neural network training. As a byproduct, we provide the $first$ provable advantage of the scheme over the iterative averaging method in the common setting.

The optimization of fuzzy grey cognitive map (FGCM) can enhance the decision quality of the system in managing uncertainties and incomplete information. Addressing this issue requires a method that effectively balances the competing demands of the speed and precision in the optimization process. Therefore, a tradeoff genetic algorithm (TOGA) is proposed to refine the FGCM optimization process in this article. First, a modified fitness function with a penalty term is designed to improve the convergence rate, which can drive the FGCM population to obtain the optimal solution during the evolutionary process. Second, an adaptive genetic mechanism based on horizontal comparison and longitudinal assessment, is designed to strike a balance between accelerating convergence and avoiding the dilemma of falling into local optima. Finally, in the simulation section, the effectiveness of the proposed method is validated by optimizing FGCM using synthetic datasets and applying it toa spacecraft debris threat avoidance scenario.

This paper focuses on the high-dimensional sampling of log-concave distributions with composite structures: $p^*(\mathrm{d}x)\propto \exp(-g(x)-f(x))\mathrm{d}x$. We develop a double randomization technique, which leads to a fast underdamped Langevin algorithm with a dimension-independent convergence guarantee. We prove that the algorithm enjoys an overall $\tilde{\mathcal{O}}\left(\frac{\left(\mathrm{tr}(H)\right)^{1/3}}{\epsilon^{2/3}}\right)$ iteration complexity to reach an $\epsilon$-tolerated sample whose distribution $p$ admits $W_2(p,p^*)\leq \epsilon$. Here, $H$ is an upper bound of the Hessian matrices for $f$ and does not explicitly depend on dimension $d$. For the posterior sampling over linear models with normalized data, we show a clear superiority of convergence rate which is dimension-free and outperforms the previous best-known results by a $d^{1/3}$ factor. The analysis to achieve a faster convergence rate brings new insights into high-dimensional sampling.