Abstract-We present and analyze methods for patrolling an environment with a distributed swarm of robots. Our approach uses a physical data structure -a distributed triangulation of the workspace. A large number of stationary "mapping" robots cover and triangulate the environment and a smaller number of mobile "patrolling" robots move amongst them. The focus of this work is to develop, analyze, implement and compare local patrolling policies. We desire strategies that achieve full coverage, but also produce good coverage frequency and visitation times. Policies that provide theoretical guarantees for these quantities have received some attention, but gaps have remained.We present: 1) A summary of how to achieve coverage by building a triangulation of the workspace, and the ensuing properties. 2) A description of simple local policies (LRV, for Least Recently Visited and LFV, for Least Frequently Visited) for achieving coverage by the patrolling robots. 3) New analytical arguments why different versions of LRV may require worstcase exponential time between visits of triangles. 4) Analytical evidence that a local implementation of LFV on the edges of the dual graph is possible in our scenario, and immensely better in the worst case. 5) Experimental and simulation validation for the practical usefulness of these policies, showing that even a small number of weak robots with weak local information can greatly outperform a single, powerful robots with full information and computational capabilities.

We explore a novel setting of the Multi-Armed Bandit (MAB) problem inspired from real world applications which we call bandits with "stochastic delayed composite anonymous feedback (SDCAF)". In SDCAF, the rewards on pulling arms are stochastic with respect to time but spread over a fixed number of time steps in the future after pulling the arm. The complexity of this problem stems from the anonymous feedback to the player and the stochastic generation of the reward. Due to the aggregated nature of the rewards, the player is unable to associate the reward to a particular time step from the past. We present two algorithms for this more complicated setting of SDCAF using phase based extensions of the UCB algorithm. We perform regret analysis to show sub-linear theoretical guarantees on both the algorithms.

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Algorithmic decision making based on computer vision and machine learning methods continues to permeate our lives. But issues related to biases of these models and the extent to which they treat certain segments of the population unfairly, have led to legitimate concerns. There is agreement that because of biases in the datasets we present to the models, a fairness-oblivious training will lead to unfair models. An interesting topic is the study of mechanisms via which the de novo design or training of the model can be informed by fairness measures. Here, we study strategies to impose fairness concurrently while training the model. While many fairness based approaches in vision rely on training adversarial modules together with the primary classification/ regression task, in an effort to remove the influence of the protected attribute or variable, we show how ideas based on well-known optimization concepts can provide a simpler alternative. In our proposal, imposing fairness just requires specifying the protected attribute and utilizing our routine. We provide a detailed technical analysis and present experiments demonstrating that various fairness measures can be reliably imposed on a number of training tasks in vision in a manner that is interpretable.

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