arXiv subjects

Kirthevasan Kandasamy

Publications and source records attributed to Kirthevasan Kandasamy.

At least 37 records · Page 2Linked to original sources

arXiv2020

Online Learning Demands in Max-min Fairness

We describe mechanisms for the allocation of a scarce resource among multiple users in a way that is efficient, fair, and strategy-proof, but when users do not know their resource requirements. The mechanism is repeated for multiple rounds and a user's requirements can change on each round. At the end of each round, users provide feedback about the allocation they received, enabling the mechanism to learn user preferences over time. Such situations are common in the shared usage of a compute cluster among many users in an organisation, where all teams may not precisely know the amount of resources needed to execute their jobs. By understating their requirements, users will receive less than they need and consequently not achieve their goals. By overstating them, they may siphon away precious resources that could be useful to others in the organisation. We formalise this task of online learning in fair division via notions of efficiency, fairness, and strategy-proofness applicable to this setting, and study this problem under three types of feedback: when the users' observations are deterministic, when they are stochastic and follow a parametric model, and when they are stochastic and nonparametric. We derive mechanisms inspired by the classical max-min fairness procedure that achieve these requisites, and quantify the extent to which they are achieved via asymptotic rates. We corroborate these insights with an experimental evaluation on synthetic problems and a web-serving task.

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arXiv2020

Tuning Hyperparameters without Grad Students: Scalable and Robust Bayesian Optimisation with Dragonfly

Bayesian Optimisation (BO) refers to a suite of techniques for global optimisation of expensive black box functions, which use introspective Bayesian models of the function to efficiently search for the optimum. While BO has been applied successfully in many applications, modern optimisation tasks usher in new challenges where conventional methods fail spectacularly. In this work, we present Dragonfly, an open source Python library for scalable and robust BO. Dragonfly incorporates multiple recently developed methods that allow BO to be applied in challenging real world settings; these include better methods for handling higher dimensional domains, methods for handling multi-fidelity evaluations when cheap approximations of an expensive function are available, methods for optimising over structured combinatorial spaces, such as the space of neural network architectures, and methods for handling parallel evaluations. Additionally, we develop new methodological improvements in BO for selecting the Bayesian model, selecting the acquisition function, and optimising over complex domains with different variable types and additional constraints. We compare Dragonfly to a suite of other packages and algorithms for global optimisation and demonstrate that when the above methods are integrated, they enable significant improvements in the performance of BO. The Dragonfly library is available at dragonfly.github.io.

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arXiv2020

Offline Contextual Bayesian Optimization for Nuclear Fusion

Nuclear fusion is regarded as the energy of the future since it presents the possibility of unlimited clean energy. One obstacle in utilizing fusion as a feasible energy source is the stability of the reaction. Ideally, one would have a controller for the reactor that makes actions in response to the current state of the plasma in order to prolong the reaction as long as possible. In this work, we make preliminary steps to learning such a controller. Since learning on a real world reactor is infeasible, we tackle this problem by attempting to learn optimal controls offline via a simulator, where the state of the plasma can be explicitly set. In particular, we introduce a theoretically grounded Bayesian optimization algorithm that recommends a state and action pair to evaluate at every iteration and show that this results in more efficient use of the simulator.

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arXiv2019

ChemBO: Bayesian Optimization of Small Organic Molecules with Synthesizable Recommendations

In applications such as molecule design or drug discovery, it is desirable to have an algorithm which recommends new candidate molecules based on the results of past tests. These molecules first need to be synthesized and then tested for objective properties. We describe ChemBO, a Bayesian optimization framework for generating and optimizing organic molecules for desired molecular properties. While most existing data-driven methods for this problem do not account for sample efficiency or fail to enforce realistic constraints on synthesizability, our approach explores the synthesis graph in a sample-efficient way and produces synthesizable candidates. We implement ChemBO as a Gaussian process model and explore existing molecular kernels for it. Moreover, we propose a novel optimal-transport based distance and kernel that accounts for graphical information explicitly. In our experiments, we demonstrate the efficacy of the proposed approach on several molecular optimization problems.

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arXiv2019

Autonomous discovery of battery electrolytes with robotic experimentation and machine-learning

Innovations in batteries take years to formulate and commercialize, requiring extensive experimentation during the design and optimization phases. We approached the design and selection of a battery electrolyte through a black-box optimization algorithm directly integrated into a robotic test-stand. We report here the discovery of a novel battery electrolyte by this experiment completely guided by the machine-learning software without human intervention. Motivated by the recent trend toward super-concentrated aqueous electrolytes for high-performance batteries, we utilize Dragonfly - a Bayesian machine-learning software package - to search mixtures of commonly used lithium and sodium salts for super-concentrated aqueous electrolytes with wide electrochemical stability windows. Dragonfly autonomously managed the robotic test-stand, recommending electrolyte designs to test and receiving experimental feedback in real time. In 40 hours of continuous experimentation over a four-dimensional design space with millions of potential candidates, Dragonfly discovered a novel, mixed-anion aqueous sodium electrolyte with a wider electrochemical stability window than state-of-the-art sodium electrolyte. A human-guided design process may have missed this optimal electrolyte. This result demonstrates the possibility of integrating robotics with machine-learning to rapidly and autonomously discover novel battery materials.

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arXiv2019

ProBO: Versatile Bayesian Optimization Using Any Probabilistic Programming Language

Optimizing an expensive-to-query function is a common task in science and engineering, where it is beneficial to keep the number of queries to a minimum. A popular strategy is Bayesian optimization (BO), which leverages probabilistic models for this task. Most BO today uses Gaussian processes (GPs), or a few other surrogate models. However, there is a broad set of Bayesian modeling techniques that could be used to capture complex systems and reduce the number of queries in BO. Probabilistic programming languages (PPLs) are modern tools that allow for flexible model definition, prior specification, model composition, and automatic inference. In this paper, we develop ProBO, a BO procedure that uses only standard operations common to most PPLs. This allows a user to drop in a model built with an arbitrary PPL and use it directly in BO. We describe acquisition functions for ProBO, and strategies for efficiently optimizing these functions given complex models or costly inference procedures. Using existing PPLs, we implement new models to aid in a few challenging optimization settings, and demonstrate these on model hyperparameter and architecture search tasks.

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arXiv2019

A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations

Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the evaluation of the functions in question are expensive. Traditional methods for multi-objective optimization, both Bayesian and otherwise, are aimed at recovering the Pareto front of these objectives. However, in certain cases a practitioner might desire to identify Pareto optimal points only in a subset of the Pareto front due to external considerations. In this work, we propose a strategy based on random scalarizations of the objectives that addresses this problem. Our approach is able to flexibly sample from desired regions of the Pareto front and, computationally, is considerably cheaper than most approaches for MOO. We also study a notion of regret in the multi-objective setting and show that our strategy achieves sublinear regret. We experiment with both synthetic and real-life problems, and demonstrate superior performance of our proposed algorithm in terms of the flexibility and regret.

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arXiv2019

Multi-fidelity Gaussian Process Bandit Optimisation

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 \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.

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arXiv2019

Neural Architecture Search with Bayesian Optimisation and Optimal Transport

Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function $f$ which is only accessible via point evaluations. It is typically used in settings where $f$ is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, only permits tuning scalar hyper-parameters of machine learning algorithms. However, with the surge of interest in deep learning, there is an increasing demand to tune neural network \emph{architectures}. In this work, we develop NASBOT, a Gaussian process based BO framework for neural architecture search. To accomplish this, we develop a distance metric in the space of neural network architectures which can be computed efficiently via an optimal transport program. This distance might be of independent interest to the deep learning community as it may find applications outside of BO. We demonstrate that NASBOT outperforms other alternatives for architecture search in several cross validation based model selection tasks on multi-layer perceptrons and convolutional neural networks.

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arXiv2018

Noisy Blackbox Optimization with Multi-Fidelity Queries: A Tree Search Approach

We study the problem of black-box optimization of a noisy function in the presence of low-cost approximations or fidelities, which is motivated by problems like hyper-parameter tuning. In hyper-parameter tuning evaluating the black-box function at a point involves training a learning algorithm on a large data-set at a particular hyper-parameter and evaluating the validation error. Even a single such evaluation can be prohibitively expensive. Therefore, it is beneficial to use low-cost approximations, like training the learning algorithm on a sub-sampled version of the whole data-set. These low-cost approximations/fidelities can however provide a biased and noisy estimate of the function value. In this work, we incorporate the multi-fidelity setup in the powerful framework of noisy black-box optimization through tree-like hierarchical partitions. We propose a multi-fidelity bandit based tree-search algorithm for the problem and provide simple regret bounds for our algorithm. Finally, we validate the performance of our algorithm on real and synthetic datasets, where it outperforms several benchmarks.

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arXiv2018

Myopic Bayesian Design of Experiments via Posterior Sampling and Probabilistic Programming

We design a new myopic strategy for a wide class of sequential design of experiment (DOE) problems, where the goal is to collect data in order to to fulfil a certain problem specific goal. Our approach, Myopic Posterior Sampling (MPS), is inspired by the classical posterior (Thompson) sampling algorithm for multi-armed bandits and leverages the flexibility of probabilistic programming and approximate Bayesian inference to address a broad set of problems. Empirically, this general-purpose strategy is competitive with more specialised methods in a wide array of DOE tasks, and more importantly, enables addressing complex DOE goals where no existing method seems applicable. On the theoretical side, we leverage ideas from adaptive submodularity and reinforcement learning to derive conditions under which MPS achieves sublinear regret against natural benchmark policies.

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arXiv2017

Asynchronous Parallel Bayesian Optimisation via Thompson Sampling

We design and analyse variations of the classical Thompson sampling (TS) procedure for Bayesian optimisation (BO) in settings where function evaluations are expensive, but can be performed in parallel. Our theoretical analysis shows that a direct application of the sequential Thompson sampling algorithm in either synchronous or asynchronous parallel settings yields a surprisingly powerful result: making $n$ evaluations distributed among $M$ workers is essentially equivalent to performing $n$ evaluations in sequence. Further, by modeling the time taken to complete a function evaluation, we show that, under a time constraint, asynchronously parallel TS achieves asymptotically lower regret than both the synchronous and sequential versions. These results are complemented by an experimental analysis, showing that asynchronous TS outperforms a suite of existing parallel BO algorithms in simulations and in a hyper-parameter tuning application in convolutional neural networks. In addition to these, the proposed procedure is conceptually and computationally much simpler than existing work for parallel BO.

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arXiv2017

Multi-fidelity Bayesian Optimisation with Continuous Approximations

Bandit methods for black-box optimisation, such as Bayesian optimisation, are used in a variety of applications including hyper-parameter tuning and experiment design. Recently, \emph{multi-fidelity} methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multi-fidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multi-fidelity methods assume only a finite number of approximations. In many practical applications however, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data $N$ and/or few training iterations $T$. Here, the approximations are best viewed as arising out of a continuous two dimensional space $(N,T)$. In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.

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arXiv2017

Batch Policy Gradient Methods for Improving Neural Conversation Models

We study reinforcement learning of chatbots with recurrent neural network architectures when the rewards are noisy and expensive to obtain. For instance, a chatbot used in automated customer service support can be scored by quality assurance agents, but this process can be expensive, time consuming and noisy. Previous reinforcement learning work for natural language processing uses on-policy updates and/or is designed for on-line learning settings. We demonstrate empirically that such strategies are not appropriate for this setting and develop an off-policy batch policy gradient method (BPG). We demonstrate the efficacy of our method via a series of synthetic experiments and an Amazon Mechanical Turk experiment on a restaurant recommendations dataset.

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arXiv2017

Query Efficient Posterior Estimation in Scientific Experiments via Bayesian Active Learning

A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments such as cosmological simulations of the universe. An urgent challenge in these research domains is to develop methods that can estimate the posterior with few likelihood evaluations. In this paper, we study active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior estimation in an active regression framework. We propose two myopic query strategies to choose where to evaluate the likelihood and implement them using Gaussian processes. Via experiments on a series of synthetic and real examples we demonstrate that our approach is significantly more query efficient than existing techniques and other heuristics for posterior estimation.

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arXiv2016

The Multi-fidelity Multi-armed Bandit

We study a variant of the classical stochastic $K$-armed bandit where observing the outcome of each arm is expensive, but cheap approximations to this outcome are available. For example, in online advertising the performance of an ad can be approximated by displaying it for shorter time periods or to narrower audiences. We formalise this task as a multi-fidelity bandit, where, at each time step, the forecaster may choose to play an arm at any one of $M$ fidelities. The highest fidelity (desired outcome) expends cost $λ^{(m)}$. The $m^{\text{th}}$ fidelity (an approximation) expends $λ^{(m)} < λ^{(M)}$ and returns a biased estimate of the highest fidelity. We develop MF-UCB, a novel upper confidence bound procedure for this setting and prove that it naturally adapts to the sequence of available approximations and costs thus attaining better regret than naive strategies which ignore the approximations. For instance, in the above online advertising example, MF-UCB would use the lower fidelities to quickly eliminate suboptimal ads and reserve the larger expensive experiments on a small set of promising candidates. We complement this result with a lower bound and show that MF-UCB is nearly optimal under certain conditions.

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arXiv2016

Learning HMMs with Nonparametric Emissions via Spectral Decompositions of Continuous Matrices

Recently, there has been a surge of interest in using spectral methods for estimating latent variable models. However, it is usually assumed that the distribution of the observations conditioned on the latent variables is either discrete or belongs to a parametric family. In this paper, we study the estimation of an $m$-state hidden Markov model (HMM) with only smoothness assumptions, such as Hölderian conditions, on the emission densities. By leveraging some recent advances in continuous linear algebra and numerical analysis, we develop a computationally efficient spectral algorithm for learning nonparametric HMMs. Our technique is based on computing an SVD on nonparametric estimates of density functions by viewing them as \emph{continuous matrices}. We derive sample complexity bounds via concentration results for nonparametric density estimation and novel perturbation theory results for continuous matrices. We implement our method using Chebyshev polynomial approximations. Our method is competitive with other baselines on synthetic and real problems and is also very computationally efficient.

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arXiv2016

Additive Approximations in High Dimensional Nonparametric Regression via the SALSA

High dimensional nonparametric regression is an inherently difficult problem with known lower bounds depending exponentially in dimension. A popular strategy to alleviate this curse of dimensionality has been to use additive models of \emph{first order}, which model the regression function as a sum of independent functions on each dimension. Though useful in controlling the variance of the estimate, such models are often too restrictive in practical settings. Between non-additive models which often have large variance and first order additive models which have large bias, there has been little work to exploit the trade-off in the middle via additive models of intermediate order. In this work, we propose SALSA, which bridges this gap by allowing interactions between variables, but controls model capacity by limiting the order of interactions. SALSA minimises the residual sum of squares with squared RKHS norm penalties. Algorithmically, it can be viewed as Kernel Ridge Regression with an additive kernel. When the regression function is additive, the excess risk is only polynomial in dimension. Using the Girard-Newton formulae, we efficiently sum over a combinatorial number of terms in the additive expansion. Via a comparison on $15$ real datasets, we show that our method is competitive against $21$ other alternatives.

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