In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Q: The goal of compressed sensing is to learn a structured signal $x$
from a limited number of noisy linear measurements $y pprox Ax$. In
traditional compressed sensing, ''structure'' is represented by
sparsity in some known basis. Inspired by the success of deep
learning in modeling images, recent work starting with~\cite{BDJP17}
has instead considered structure to come from a generative model
$G: \R^k o \R^n$. We present two results establishing the
difficulty of this latter task, showing that existing bounds are
tight.

First, we provide a lower bound matching the~\cite{BDJP17} upper
bound for compressed sensing from $L$-Lipschitz generative models
$G$. In particular, there exists such a function that requires
roughly $\Omega(k \log L)$ linear measurements for sparse recovery
to be possible. This holds even for the more relaxed goal of
\emph{nonuniform} recovery.

Second, we show that generative models generalize sparsity as a
representation of structure. In particular, we construct a
ReLU-based neural network $G: \R^{2k} o \R^n$ with $O(1)$ layers
and $O(kn)$ activations per layer, such that the range of $G$
contains all $k$-sparse vectors.

A: Lower bound for compressed sensing w/ generative models that matches known upper bounds
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Q: Reinforcement learning in multi-agent scenarios is important for real-world applications but presents challenges beyond those seen in single-agent settings. We present an actor-critic algorithm that trains decentralized policies in multi-agent settings, using centrally computed critics that share an attention mechanism which selects relevant information for each agent at every timestep. This attention mechanism enables more effective and scalable learning in complex multi-agent environments, when compared to recent approaches. Our approach is applicable not only to cooperative settings with shared rewards, but also individualized reward settings, including adversarial settings, and it makes no assumptions about the action spaces of the agents. As such, it is flexible enough to be applied to most multi-agent learning problems

A: We propose an approach to learn decentralized policies in multi-agent settings using attention-based critics and demonstrate promising results in environments with complex interactions.
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Q: Distributed optimization is vital in solving large-scale machine learning problems. A widely-shared feature of distributed optimization techniques is the requirement that all nodes complete their assigned tasks in each computational epoch before the system can proceed to the next epoch. In such settings, slow nodes, called stragglers, can greatly slow progress. To mitigate the impact of stragglers, we propose an online distributed optimization method called Anytime Minibatch. In this approach, all nodes are given a fixed time to compute the gradients of as many data samples as possible. The result is a variable per-node minibatch size. Workers then get a fixed communication time to average their minibatch gradients via several rounds of consensus, which are then used to update primal variables via dual averaging. Anytime Minibatch prevents stragglers from holding up the system without wasting the work that stragglers can complete. We present a convergence analysis and analyze the wall time performance. Our numerical results show that our approach is up to 1.5 times faster in Amazon EC2 and it is up to five times faster when there is greater variability in compute node performance.

A:
Accelerate distributed optimization by exploiting stragglers.
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