Roughly a year ago, Latent AI, a now three-year-old, Menlo Park, California-based startup, pitched a handful of investors during TechCrunch's Battlefield competition. It didn't win that contest, but that hasn't kept it from winning the interest of investors elsewhere. It just closed on $19 million in Series A funding in a round co-led by Future Ventures and Blackhorn Ventures, with participation from Booz Allen, Lockheed Martin, 40 North Ventures, and Autotech Ventures. The company has now raised $22.5 million altogether. Steve Jurvetson, the veteran investor and co-founder of Future Ventures, says of possible applications to think of "face-detection algorithms running locally within security cameras or appliances, or Siri-like voice interfaces working instantly," even when there's no network connectivity.

We study exploration in stochastic multi-armed bandits when we have access to a divisible resource, and can allocate varying amounts of this resource to arm pulls. By allocating more resources to a pull, we can compute the outcome faster to inform subsequent decisions about which arms to pull. However, since distributed environments do not scale linearly, executing several arm pulls in parallel, and hence less resources per pull, may result in better throughput. For example, in simulation-based scientific studies, an expensive simulation can be sped up by running it on multiple cores. This speed-up is, however, partly offset by the communication among cores and overheads, which results in lower throughput than if fewer cores were allocated to run more trials in parallel. We explore these trade-offs in the fixed confidence setting, where we need to find the best arm with a given success probability, while minimizing the time to do so. We propose an algorithm which trades off between information accumulation and throughout and show that the time taken can be upper bounded by the solution of a dynamic program whose inputs are the squared gaps between the suboptimal and optimal arms. We prove a matching hardness result which demonstrates that the above dynamic program is fundamental to this problem. Next, we propose and analyze an algorithm for the fixed deadline setting, where we are given a time deadline and need to maximize the success probability of finding the best arm. We corroborate these theoretical insights with an empirical evaluation.

In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour and achieves better bounds on the regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

This paper presents a novel decentralized high-dimensional Bayesian optimization (DEC-HBO) algorithm that, in contrast to existing HBO algorithms, can exploit the interdependent effects of various input components on the output of the unknown objective function f for boosting the BO performance and still preserve scalability in the number of input dimensions without requiring prior knowledge or the existence of a low (effective) dimension of the input space. To realize this, we propose a sparse yet rich factor graph representation of f to be exploited for designing an acquisition function that can be similarly represented by a sparse factor graph and hence be efficiently optimized in a decentralized manner using distributed message passing. Despite richly characterizing the interdependent effects of the input components on the output of f with a factor graph, DEC-HBO can still guarantee no-regret performance asymptotically. Empirical evaluation on synthetic and real-world experiments (e.g., sparse Gaussian process model with 1811 hyperparameters) shows that DEC-HBO outperforms the state-of-the-art HBO algorithms.

This paper presents a novel decentralized high-dimensional Bayesian optimization (DEC-HBO) algorithm that, in contrast to existing HBO algorithms, can exploit the interdependent effects of various input components on the output of the unknown objective function f for boosting the BO performance and still preserve scalability in the number of input dimensions without requiring prior knowledge or the existence of a low (effective) dimension of the input space. To realize this, we propose a sparse yet rich factor graph representation of f to be exploited for designing an acquisition function that can be similarly represented by a sparse factor graph and hence be efficiently optimized in a decentralized manner using distributed message passing. Despite richly characterizing the interdependent effects of the input components on the output of f with a factor graph, DEC-HBO can still guarantee no-regret performance asymptotically. Empirical evaluation on synthetic and real-world experiments (e.g., sparse Gaussian process model with 1811 hyperparameters) shows that DEC-HBO outperforms the state-of-the-art HBO algorithms.

In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function $f$. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to $f$ may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of $f$ in a small but promising region and speedily identify the optimum. We formalise this task as a \emph{multi-fidelity} bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.