We investigate the problem of minimizing the excess generalization error with respect to the best expert prediction in a finite family in the stochastic setting, under limited access to information. We assume that the learner only has access to a limited number of expert advices per training round, as well as for prediction. Assuming that the loss function is Lipschitz and strongly convex, we show that if we are allowed to see the advice of only one expert per round for T rounds in the training phase, or to use the advice of only one expert for prediction in the test phase, the worst-case excess risk is Ω(1/ T) with probability lower bounded by a constant. However, if we are allowed to see at least two actively chosen expert advices per training round and use at least two experts for prediction, the fast rate O(1/T) can be achieved. We design novel algorithms achieving this rate in this setting, and in the setting where the learner has a budget constraint on the total number of observed expert advices, and give precise instance-dependent bounds on the number of training rounds and queries needed to achieve a given generalization error precision.

Federated learning (FL) is an effective machine learning paradigm where multiple clients can train models based on heterogeneous data in a decentralized manner without accessing their private data. However, existing FL systems undergo performance deterioration due to feature-level test-time shifts, which are well investigated in centralized settings but rarely studied in FL. The common non-IID issue in FL usually refers to inter-client heterogeneity during training phase, while the test-time shift refers to the intra-client heterogeneity during test phase. Although the former is always deemed to be notorious for FL, there is still a wealth of useful information delivered by heterogeneous data sources, which may potentially help alleviate the latter issue. To explore the possibility of using inter-client heterogeneity in handling intra-client heterogeneity, we firstly propose a contrastive learning-based FL framework, namely FedICON, to capture invariant knowledge among heterogeneous clients and consistently tune the model to adapt to test data. In FedICON, each client performs sample-wise supervised contrastive learning during the local training phase, which enhances sample-wise invariance encoding ability. Through global aggregation, the invariance extraction ability can be mutually boosted among inter-client heterogeneity. During the test phase, our test-time adaptation procedure leverages unsupervised contrastive learning to guide the model to smoothly generalize to test data under intra-client heterogeneity. Extensive experiments validate the effectiveness of the proposed FedICON in taming heterogeneity to handle test-time shift problems.

FL framework, namely FedICON, to capture invariant knowledge among heterogeneous clients and consistently tune the model to adapt to test data.

Multi-agent reinforcement learning (MARL) has recently received considerable attention due to its applicability to a wide range of real-world applications.