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Representation learning is a powerful tool that enables learning over large multitudes of agents or domains by enforcing that all agents operate on a shared set of learned features. However, many robotics or controls applications that would benefit from collaboration operate in settings with changing environments and goals, whereas most guarantees for representation learning are stated for static settings. Toward rigorously establishing the benefit of representation learning in dynamic settings, we analyze the regret of multi-task representation learning for linear-quadratic control. This setting introduces unique challenges. Firstly, we must account for and balance the misspecification introduced by an approximate representation. Secondly, we cannot rely on the parameter update schemes of single-task online LQR, for which least-squares often suffices, and must devise a novel scheme to ensure sufficient improvement. We demonstrate that for settings where exploration is benign, the regret of any agent after T timesteps scales with the square root of T/H, where H is the number of agents. In settings with difficult exploration, the regret scales as the square root of the input dimension times the parameter dimension multiplied by T, plus a term which scales with T to the three quarters divided by H to the one fifth. In both cases, by comparing to the minimax single-task regret, we see a benefit of a large number of agents. Notably, in the difficult exploration case, by sharing a representation across tasks, the effective task-specific parameter count can often be small. Lastly, we validate the trends we predict. 

As GPU-using tasks become more common in embedded, safety-critical systems, efficiency demands necessitate sharing a single GPU among multiple tasks. Unfortunately, existing ways to schedule multiple tasks onto a GPU often either result in a loss of ability to meet deadlines, or a loss of efficiency. In this work, we develop a system-level spatial compute partitioning mechanism for NVIDIA GPUs and demonstrate that it can be used to execute tasks efficiently without compromising timing predictability. Our tool, called nvtaskset, supports composable systems by not requiring task, driver, or hardware modifications. In our evaluation, we demonstrate sub-1-μs overheads, stronger partition enforcement, and finer-granularity partitioning when using our mechanism instead of NVIDIA’s Multi-Process Service (MPS) or Multi-instance GPU (MiG) features. 

Abstract We characterize Borel line graphs in terms of 10 forbidden induced subgraphs, namely the nine finite graphs from the classical result of Beineke together with a 10th infinite graph associated with the equivalence relation$$\mathbb {E}_0$$on the Cantor space. As a corollary, we prove a partial converse to the Feldman–Moore theorem, which allows us to characterize all locally countable Borel line graphs in terms of their Borel chromatic numbers.