In decentralized multi-agent reinforcement learning, agents learning in isolation can lead to relative over-generalization (RO), where optimal joint actions are undervalued in favor of suboptimal ones. This hinders effective coordination in cooperative tasks, as agents tend to choose actions that are individually rational but collectively suboptimal. To address this issue, we introduce MaxMax Q-Learning (MMQ), which employs an iterative process of sampling and evaluating potential next states, selecting those with maximal Q-values for learning. This approach refines approximations of ideal state transitions, aligning more closely with the optimal joint policy of collaborating agents. We provide theoretical analysis supporting MMQ's potential and present empirical evaluations across various environments susceptible to RO. Our results demonstrate that MMQ frequently outperforms existing baselines, exhibiting enhanced convergence and sample efficiency.

\textit{Relative overgeneralization} (RO) occurs in cooperative multi-agent learning tasks when agents converge towards a suboptimal joint policy due to overfitting to suboptimal behavior of other agents. In early work, optimism has been shown to mitigate the \textit{RO} problem when using tabular Q-learning. However, with function approximation optimism can amplify overestimation and thus fail on complex tasks. On the other hand, recent deep multi-agent policy gradient (MAPG) methods have succeeded in many complex tasks but may fail with severe \textit{RO}. We propose a general, yet simple, framework to enable optimistic updates in MAPG methods and alleviate the RO problem. Specifically, we employ a \textit{Leaky ReLU} function where a single hyperparameter selects the degree of optimism to reshape the advantages when updating the policy. Intuitively, our method remains optimistic toward individual actions with lower returns which are potentially caused by other agents' sub-optimal behavior during learning. The optimism prevents the individual agents from quickly converging to a local optimum. We also provide a formal analysis from an operator view to understand the proposed advantage transformation. In extensive evaluations on diverse sets of tasks, including illustrative matrix games, complex \textit{Multi-agent MuJoCo} and \textit{Overcooked} benchmarks, the proposed method\footnote{Code can be found at \url{https://github.com/wenshuaizhao/optimappo}.} outperforms strong baselines on 13 out of 19 tested tasks and matches the performance on the rest.

We propose a novel discrete-time dynamical system-based framework for achieving adversarial robustness in machine learning models. Our algorithm is originated from robust optimization, which aims to find the saddle point of a min-max optimization problem in the presence of uncertainties. The robust learning problem is formulated as a robust optimization problem, and we introduce a discrete-time algorithm based on a saddle-point dynamical system (SDS) to solve this problem. Under the assumptions that the cost function is convex and uncertainties enter concavely in the robust learning problem, we analytically show that using a diminishing step-size, the stochastic version of our algorithm, SSDS converges asymptotically to the robust optimal solution. The algorithm is deployed for the training of adversarially robust deep neural networks. Although such training involves highly non-convex non-concave robust optimization problems, empirical results show that the algorithm can achieve significant robustness for deep learning. We compare the performance of our SSDS model to other state-of-the-art robust models, e.g., trained using the projected gradient descent (PGD)-training approach. From the empirical results, we find that SSDS training is computationally inexpensive (compared to PGD-training) while achieving comparable performances. SSDS training also helps robust models to maintain a relatively high level of performance for clean data as well as under black-box attacks.