For both problems, the classical performance measure is the learner's (static) regret, defined as the difference between the learner's total loss and the loss of the best fixed action.

This paper studies online convex optimization in dynamic environments, where one wishes to control the regret with respect to sequences of comparators, as opposed to a static comparator. The complexity of a comparator sequence is measured by its path length P_T, and the goal is to obtain an optimal regret bound simultaneously for all path lengths. A first bound in this setting was established in the pioneering paper [1], which showed that online gradient descent (OGD, projected on the convex compact domain) with step-size 1/sqrt(T) achieves an at most T {1/2} (1 P_T) regret for all comparator sequences. However, there is a gap between this upper bound and the (T (1 P_T)) {1/2} lower bound on worst-case regret established in Theorem 2 of the present paper, which is the first lower bound for this problem. On the other hand, if the path length P_T one wishes to compare against is known in advance, optimally tuning the step-size of OGD with respect to P_T in the OGD regret bound yields optimal (T (1 P_T)) {1/2} regret for this path length.

Recently a line of researches has delved the use of graph neural networks (GNNs) for decentralized control in swarm robotics. However, it has been observed that relying solely on the states of immediate neighbors is insufficient to imitate a centralized control policy. To address this limitation, prior studies proposed incorporating $L$-hop delayed states into the computation. While this approach shows promise, it can lead to a lack of consensus among distant flock members and the formation of small clusters, consequently resulting in the failure of cohesive flocking behaviors. Instead, our approach leverages spatiotemporal GNN, named STGNN that encompasses both spatial and temporal expansions. The spatial expansion collects delayed states from distant neighbors, while the temporal expansion incorporates previous states from immediate neighbors. The broader and more comprehensive information gathered from both expansions results in more effective and accurate predictions. We develop an expert algorithm for controlling a swarm of robots and employ imitation learning to train our decentralized STGNN model based on the expert algorithm. We simulate the proposed STGNN approach in various settings, demonstrating its decentralized capacity to emulate the global expert algorithm. Further, we implemented our approach to achieve cohesive flocking, leader following and obstacle avoidance by a group of Crazyflie drones. The performance of STGNN underscores its potential as an effective and reliable approach for achieving cohesive flocking, leader following and obstacle avoidance tasks.

We consider an MDP setting in which the reward function is allowed to change during each time step of play (possibly in an adversarial manner), yet the dynamics remain fixed. Similar to the experts setting, we address the question of how well can an agent do when compared to the reward achieved under the best stationary policy over time. We provide efficient algorithms, which have regret bounds with no dependence on the size of state space. Instead, these bounds depend only on a certain horizon time of the process and logarithmically on the number of actions. We also show that in the case that the dynamics change over time, the problem becomes computationally hard.

In online convex optimization, the player aims to minimize regret, or the difference between her loss and that of the best fixed decision in hindsight over the entire repeated game. Algorithms that minimize (standard) regret may converge to a fixed decision, which is undesirable in changing or dynamic environments. This motivates the stronger metrics of performance, notably adaptive and dynamic regret. Adaptive regret is the maximum regret over any continuous sub-interval in time. Dynamic regret is the difference between the total cost and that of the best sequence of decisions in hindsight. State-of-the-art performance in both adaptive and dynamic regret minimization suffers a computational penalty - typically on the order of a multiplicative factor that grows logarithmically in the number of game iterations. In this paper we show how to reduce this computational penalty to be doubly logarithmic in the number of game iterations, and retain near optimal adaptive and dynamic regret bounds.

In this paper, we develop a learning-based approach for decentralized submodular maximization. We focus on applications where robots are required to jointly select actions, e.g., motion primitives, to maximize team submodular objectives with local communications only. Such applications are essential for large-scale multi-robot coordination such as multi-robot motion planning for area coverage, environment exploration, and target tracking. But the current decentralized submodular maximization algorithms either require assumptions on the inter-robot communication or lose some suboptimal guarantees. In this work, we propose a general-purpose learning architecture towards submodular maximization at scale, with decentralized communications. Particularly, our learning architecture leverages a graph neural network (GNN) to capture local interactions of the robots and learns decentralized decision-making for the robots. We train the learning model by imitating an expert solution and implement the resulting model for decentralized action selection involving local observations and communications only. We demonstrate the performance of our GNN-based learning approach in a scenario of active target coverage with large networks of robots. The simulation results show our approach nearly matches the coverage performance of the expert algorithm, and yet runs several orders faster with more than 30 robots. The results also exhibit our approach's generalization capability in previously unseen scenarios, e.g., larger environments and larger networks of robots.

Efficient and collision-free navigation in multi-robot systems is fundamental to advancing mobility. Scenarios where the robots are restricted in observation and communication range call for decentralized solutions, whereby robots execute localized planning policies. From the point of view of an individual robot, however, its local decision-making system is incomplete, since other agents' unobservable states affect future values. The manner in which information is shared is crucial to the system's performance, yet is not well addressed by current approaches. To address these challenges, we propose a combined architecture, with the goal of learning a decentralized sequential action policy that yields efficient path plans for all robots. Our framework is composed of a convolutional neural network (CNN) that extracts adequate features from local observations, and a graph neural network (GNN) that communicates these features among robots. We train the model to imitate an expert algorithm, and use the resulting model online in decentralized planning involving only local communication. We evaluate our method in simulations involving teams of robots in cluttered workspaces. We measure the success rates and sum of costs over the planned paths. The results show a performance close to that of our expert algorithm, demonstrating the validity of our approach. In particular, we show our model's capability to generalize to previously unseen cases (involving larger environments and larger robot teams).

We study methods for improving fairness to subgroups in settings with overlapping populations and sequential predictions. Classical notions of fairness focus on the balance of some property across different populations. However, in many applications the goal of the different groups is not to be predicted equally but rather to be predicted well. We demonstrate that the task of satisfying this guarantee for multiple overlapping groups is not straightforward and show that for the simple objective of unweighted average of false negative and false positive rate, satisfying this for overlapping populations can be statistically impossible even when we are provided predictors that perform well separately on each subgroup. On the positive side, we show that when individuals are equally important to the different groups they belong to, this goal is achievable; to do so, we draw a connection to the sleeping experts literature in online learning. Motivated by the one-sided feedback in natural settings of interest, we extend our results to such a feedback model. We also provide a game-theoretic interpretation of our results, examining the incentives of participants to join the system and to provide the system full information about predictors they may possess. We end with several interesting open problems concerning the strength of guarantees that can be achieved in a computationally efficient manner.

Past research has studied two approaches to utilise predefined policy sets in repeated interactions: as experts, to dictate our own actions, and as types, to characterise the behaviour of other agents. In this work, we bring these complementary views together in the form of a novel meta-algorithm, called Expert-HBA (E-HBA), which can be applied to any expert algorithm that considers the average (or total) payoff an expert has yielded in the past. E-HBA gradually mixes the past payoff with a predicted future payoff, which is computed using the type-based characterisation. We present results from a comprehensive set of repeated matrix games, comparing the performance of several well-known expert algorithms with and without the aid of E-HBA. Our results show that E-HBA has the potential to significantly improve the performance of expert algorithms.

We consider online algorithms under both the competitive ratio criteria and the regret minimization one. Our main goal is to build a unified methodology that would be able to guarantee both criteria simultaneously. For a general class of online algorithms, namely any Metrical Task System (MTS), we show that one can simultaneously guarantee the best known competitive ratio and a natural regret bound. For the paging problem we further show an efficient online algorithm (polynomial in the number of pages) with this guarantee. To this end, we extend an existing regret minimization algorithm (specifically, Kapralov and Panigrahy) to handle movement cost (the cost of switching between states of the online system). We then show how to use the extended regret minimization algorithm to combine multiple online algorithms. Our end result is an online algorithm that can combine a "base" online algorithm, having a guaranteed competitive ratio, with a range of online algorithms that guarantee a small regret over any interval of time. The combined algorithm guarantees both that the competitive ratio matches that of the base algorithm and a low regret over any time interval. As a by product, we obtain an expert algorithm with close to optimal regret bound on every time interval, even in the presence of switching costs. This result is of independent interest.