arXiv subjects

Sunil Gupta

Publications and source records attributed to Sunil Gupta.

At least 91 records · Page 5Linked to original sources

arXiv2020

Learning Transferable Domain Priors for Safe Exploration in Reinforcement Learning

Prior access to domain knowledge could significantly improve the performance of a reinforcement learning agent. In particular, it could help agents avoid potentially catastrophic exploratory actions, which would otherwise have to be experienced during learning. In this work, we identify consistently undesirable actions in a set of previously learned tasks, and use pseudo-rewards associated with them to learn a prior policy. In addition to enabling safer exploratory behaviors in subsequent tasks in the domain, we show that these priors are transferable to similar environments, and can be learned off-policy and in parallel with the learning of other tasks in the domain. We compare our approach to established, state-of-the-art algorithms in both discrete as well as continuous environments, and demonstrate that it exhibits a safer exploratory behavior while learning to perform arbitrary tasks in the domain. We also present a theoretical analysis to support these results, and briefly discuss the implications and some alternative formulations of this approach, which could also be useful in certain scenarios.

cs.AI↗

arXiv2020

From deep to Shallow: Equivalent Forms of Deep Networks in Reproducing Kernel Krein Space and Indefinite Support Vector Machines

In this paper we explore a connection between deep networks and learning in reproducing kernel Krein space. Our approach is based on the concept of push-forward - that is, taking a fixed non-linear transform on a linear projection and converting it to a linear projection on the output of a fixed non-linear transform, pushing the weights forward through the non-linearity. Applying this repeatedly from the input to the output of a deep network, the weights can be progressively "pushed" to the output layer, resulting in a flat network that has the form of a fixed non-linear map (whose form is determined by the structure of the deep network) followed by a linear projection determined by the weight matrices - that is, we take a deep network and convert it to an equivalent (indefinite) kernel machine. We then investigate the implications of this transformation for capacity control and uniform convergence, and provide a Rademacher complexity bound on the deep network in terms of Rademacher complexity in reproducing kernel Krein space. Finally, we analyse the sparsity properties of the flat representation, showing that the flat weights are (effectively) Lp-"norm" regularised with 0<p<1 (bridge regression).

stat.ML↗

arXiv2020

Sequential Subspace Search for Functional Bayesian Optimization Incorporating Experimenter Intuition

We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity etc.) of the optimal solution encoded into the covariance function of a Gaussian Process. Our algorithm generates a sequence of finite-dimensional random subspaces of functional space spanned by a set of draws from the experimenter's Gaussian Process. Standard Bayesian optimisation is applied on each subspace, and the best solution found used as a starting point (origin) for the next subspace. Using the concept of effective dimensionality, we analyse the convergence of our algorithm and provide a regret bound to show that our algorithm converges in sub-linear time provided a finite effective dimension exists. We test our algorithm in simulated and real-world experiments, namely blind function matching, finding the optimal precipitation-strengthening function for an aluminium alloy, and learning rate schedule optimisation for deep networks.

cs.LG↗

arXiv2020

Trading Convergence Rate with Computational Budget in High Dimensional Bayesian Optimization

Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find global maximisation of acquisition function, which itself is a non-convex optimization problem in the original search space. With growing dimensions, the computational budget for this maximisation gets increasingly short leading to inaccurate solution of the maximisation. This inaccuracy adversely affects both the convergence and the efficiency of BO. We propose a novel approach where the acquisition function only requires maximisation on a discrete set of low dimensional subspaces embedded in the original high-dimensional search space. Our method is free of any low dimensional structure assumption on the function unlike many recent high-dimensional BO methods. Optimising acquisition function in low dimensional subspaces allows our method to obtain accurate solutions within limited computational budget. We show that in spite of this convenience, our algorithm remains convergent. In particular, cumulative regret of our algorithm only grows sub-linearly with the number of iterations. More importantly, as evident from our regret bounds, our algorithm provides a way to trade the convergence rate with the number of subspaces used in the optimisation. Finally, when the number of subspaces is "sufficiently large", our algorithm's cumulative regret is at most $\mathcal{O}^{*}(\sqrt{Tγ_T})$ as opposed to $\mathcal{O}^{*}(\sqrt{DTγ_T})$ for the GP-UCB of Srinivas et al. (2012), reducing a crucial factor $\sqrt{D}$ where $D$ being the dimensional number of input space.

stat.ML↗

arXiv2020

Bayesian Optimization with Missing Inputs

Bayesian optimization (BO) is an efficient method for optimizing expensive black-box functions. In real-world applications, BO often faces a major problem of missing values in inputs. The missing inputs can happen in two cases. First, the historical data for training BO often contain missing values. Second, when performing the function evaluation (e.g. computing alloy strength in a heat treatment process), errors may occur (e.g. a thermostat stops working) leading to an erroneous situation where the function is computed at a random unknown value instead of the suggested value. To deal with this problem, a common approach just simply skips data points where missing values happen. Clearly, this naive method cannot utilize data efficiently and often leads to poor performance. In this paper, we propose a novel BO method to handle missing inputs. We first find a probability distribution of each missing value so that we can impute the missing value by drawing a sample from its distribution. We then develop a new acquisition function based on the well-known Upper Confidence Bound (UCB) acquisition function, which considers the uncertainty of imputed values when suggesting the next point for function evaluation. We conduct comprehensive experiments on both synthetic and real-world applications to show the usefulness of our method.

cs.LG↗

arXiv2020

DeepCoDA: personalized interpretability for compositional health data

Interpretability allows the domain-expert to directly evaluate the model's relevance and reliability, a practice that offers assurance and builds trust. In the healthcare setting, interpretable models should implicate relevant biological mechanisms independent of technical factors like data pre-processing. We define personalized interpretability as a measure of sample-specific feature attribution, and view it as a minimum requirement for a precision health model to justify its conclusions. Some health data, especially those generated by high-throughput sequencing experiments, have nuances that compromise precision health models and their interpretation. These data are compositional, meaning that each feature is conditionally dependent on all other features. We propose the Deep Compositional Data Analysis (DeepCoDA) framework to extend precision health modelling to high-dimensional compositional data, and to provide personalized interpretability through patient-specific weights. Our architecture maintains state-of-the-art performance across 25 real-world data sets, all while producing interpretations that are both personalized and fully coherent for compositional data.

cs.LG↗

arXiv2020

Scalable Backdoor Detection in Neural Networks

Recently, it has been shown that deep learning models are vulnerable to Trojan attacks, where an attacker can install a backdoor during training time to make the resultant model misidentify samples contaminated with a small trigger patch. Current backdoor detection methods fail to achieve good detection performance and are computationally expensive. In this paper, we propose a novel trigger reverse-engineering based approach whose computational complexity does not scale with the number of labels, and is based on a measure that is both interpretable and universal across different network and patch types. In experiments, we observe that our method achieves a perfect score in separating Trojaned models from pure models, which is an improvement over the current state-of-the art method.

cs.CV↗

arXiv2020

Sparse Spectrum Gaussian Process for Bayesian Optimization

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this particular form of sparse approximations generates an overconfident GP, i.e. it produces less epistemic uncertainty than the original GP. Since the balance between predictive mean and the predictive variance is the key determinant to the success of Bayesian optimization, the current sparse spectrum methods are less suitable for it. We derive a new regularized marginal likelihood for finding the optimal frequencies to fix this over-confidence issue, particularly for Bayesian optimization. The regularizer trades off the accuracy in the model fitting with a targeted increase in the predictive variance of the resultant GP. Specifically, we use the entropy of the global maximum distribution from the posterior GP as the regularizer that needs to be maximized. Since this distribution cannot be calculated analytically, we first propose a Thompson sampling based approach and then a more efficient sequential Monte Carlo based approach to estimate it. Later, we also show that the Expected Improvement acquisition function can be used as a proxy for the maximum distribution, thus making the whole process further efficient. Experiments show considerable improvement to Bayesian optimization convergence rate over the vanilla sparse spectrum method and over a full GP when its covariance matrix is ill-conditioned due to the presence of a large number of observations.

cs.LG↗

arXiv2020

Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisation

In order to improve the performance of Bayesian optimisation, we develop a modified Gaussian process upper confidence bound (GP-UCB) acquisition function. This is done by sampling the exploration-exploitation trade-off parameter from a distribution. We prove that this allows the expected trade-off parameter to be altered to better suit the problem without compromising a bound on the function's Bayesian regret. We also provide results showing that our method achieves better performance than GP-UCB in a range of real-world and synthetic problems.

cs.LG↗

arXiv2020

Incorporating Expert Prior in Bayesian Optimisation via Space Warping

Bayesian optimisation is a well-known sample-efficient method for the optimisation of expensive black-box functions. However when dealing with big search spaces the algorithm goes through several low function value regions before reaching the optimum of the function. Since the function evaluations are expensive in terms of both money and time, it may be desirable to alleviate this problem. One approach to subside this cold start phase is to use prior knowledge that can accelerate the optimisation. In its standard form, Bayesian optimisation assumes the likelihood of any point in the search space being the optimum is equal. Therefore any prior knowledge that can provide information about the optimum of the function would elevate the optimisation performance. In this paper, we represent the prior knowledge about the function optimum through a prior distribution. The prior distribution is then used to warp the search space in such a way that space gets expanded around the high probability region of function optimum and shrinks around low probability region of optimum. We incorporate this prior directly in function model (Gaussian process), by redefining the kernel matrix, which allows this method to work with any acquisition function, i.e. acquisition agnostic approach. We show the superiority of our method over standard Bayesian optimisation method through optimisation of several benchmark functions and hyperparameter tuning of two algorithms: Support Vector Machine (SVM) and Random forest.

cs.LG↗

arXiv2020

Incorporating Expert Prior Knowledge into Experimental Design via Posterior Sampling

Scientific experiments are usually expensive due to complex experimental preparation and processing. Experimental design is therefore involved with the task of finding the optimal experimental input that results in the desirable output by using as few experiments as possible. Experimenters can often acquire the knowledge about the location of the global optimum. However, they do not know how to exploit this knowledge to accelerate experimental design. In this paper, we adopt the technique of Bayesian optimization for experimental design since Bayesian optimization has established itself as an efficient tool for optimizing expensive black-box functions. Again, it is unknown how to incorporate the expert prior knowledge about the global optimum into Bayesian optimization process. To address it, we represent the expert knowledge about the global optimum via placing a prior distribution on it and we then derive its posterior distribution. An efficient Bayesian optimization approach has been proposed via posterior sampling on the posterior distribution of the global optimum. We theoretically analyze the convergence of the proposed algorithm and discuss the robustness of incorporating expert prior. We evaluate the efficiency of our algorithm by optimizing synthetic functions and tuning hyperparameters of classifiers along with a real-world experiment on the synthesis of short polymer fiber. The results clearly demonstrate the advantages of our proposed method.

stat.ML↗

arXiv2020

Bayesian functional optimisation with shape prior

Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a functional optimisation problem. We develop a novel Bayesian optimisation framework for such functional optimisation of expensive black-box processes. We represent the control function using Bernstein polynomial basis and optimise in the coefficient space. We derive the theory and practice required to dynamically adjust the order of the polynomial degree, and show how prior information about shape can be integrated. We demonstrate the effectiveness of our approach for short polymer fibre design and optimising learning rate schedules for deep networks.

cs.LG↗

arXiv2020

Accelerated Bayesian Optimization throughWeight-Prior Tuning

Bayesian optimization (BO) is a widely-used method for optimizing expensive (to evaluate) problems. At the core of most BO methods is the modeling of the objective function using a Gaussian Process (GP) whose covariance is selected from a set of standard covariance functions. From a weight-space view, this models the objective as a linear function in a feature space implied by the given covariance K, with an arbitrary Gaussian weight prior ${\bf w} \sim \mathcal{N} ({\bf 0}, {\bf I})$. In many practical applications there is data available that has a similar (covariance) structure to the objective, but which, having different form, cannot be used directly in standard transfer learning. In this paper we show how such auxiliary data may be used to construct a GP covariance corresponding to a more appropriate weight prior for the objective function. Building on this, we show that we may accelerate BO by modeling the objective function using this (learned) weight prior, which we demonstrate on both test functions and a practical application to short-polymer fibre manufacture.

stat.ML↗

arXiv2020

Distributionally Robust Bayesian Quadrature Optimization

Bayesian quadrature optimization (BQO) maximizes the expectation of an expensive black-box integrand taken over a known probability distribution. In this work, we study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples. A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set. Though Monte Carlo estimate is unbiased, it has high variance given a small set of samples; thus can result in a spurious objective function. We adopt the distributionally robust optimization perspective to this problem by maximizing the expected objective under the most adversarial distribution. In particular, we propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose. We demonstrate the empirical effectiveness of our proposed framework in synthetic and real-world problems, and characterize its theoretical convergence via Bayesian regret.

cs.LG↗

arXiv2019

Bayesian Optimization for Categorical and Category-Specific Continuous Inputs

Many real-world functions are defined over both categorical and category-specific continuous variables and thus cannot be optimized by traditional Bayesian optimization (BO) methods. To optimize such functions, we propose a new method that formulates the problem as a multi-armed bandit problem, wherein each category corresponds to an arm with its reward distribution centered around the optimum of the objective function in continuous variables. Our goal is to identify the best arm and the maximizer of the corresponding continuous function simultaneously. Our algorithm uses a Thompson sampling scheme that helps connecting both multi-arm bandit and BO in a unified framework. We extend our method to batch BO to allow parallel optimization when multiple resources are available. We theoretically analyze our method for convergence and prove sub-linear regret bounds. We perform a variety of experiments: optimization of several benchmark functions, hyper-parameter tuning of a neural network, and automatic selection of the best machine learning model along with its optimal hyper-parameters (a.k.a automated machine learning). Comparisons with other methods demonstrate the effectiveness of our proposed method.

cs.LG↗

arXiv2019

Multi-objective Bayesian optimisation with preferences over objectives

We present a multi-objective Bayesian optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type "objective A is more important than objective B". These preferences are defined based on the stability of the obtained solutions with respect to preferred objective functions. Rather than attempting to find a representative subset of the complete Pareto front, our algorithm selects those Pareto-optimal points that satisfy these constraints. We formulate a new acquisition function based on expected improvement in dominated hypervolume (EHI) to ensure that the subset of Pareto front satisfying the constraints is thoroughly explored. The hypervolume calculation is weighted by the probability of a point satisfying the constraints from a gradient Gaussian Process model. We demonstrate our algorithm on both synthetic and real-world problems.

cs.LG↗

arXiv2019

Bayesian Optimization with Unknown Search Space

Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that in iterative expansions of the search space, our method can find a point whose function value within epsilon of the objective function maximum. Without the need to specify any parameters, our algorithm automatically triggers a minimal expansion required iteratively. We derive analytic expressions for when to trigger the expansion and by how much to expand. We also provide theoretical analysis to show that our method achieves epsilon-accuracy after a finite number of iterations. We demonstrate our method on both benchmark test functions and machine learning hyper-parameter tuning tasks and demonstrate that our method outperforms baselines.

stat.ML↗

arXiv2019

Cost-aware Multi-objective Bayesian optimisation

The notion of expense in Bayesian optimisation generally refers to the uniformly expensive cost of function evaluations over the whole search space. However, in some scenarios, the cost of evaluation for black-box objective functions is non-uniform since different inputs from search space may incur different costs for function evaluations. We introduce a cost-aware multi-objective Bayesian optimisation with non-uniform evaluation cost over objective functions by defining cost-aware constraints over the search space. The cost-aware constraints are a sorted tuple of indexes that demonstrate the ordering of dimensions of the search space based on the user's prior knowledge about their cost of usage. We formulate a new multi-objective Bayesian optimisation acquisition function with detailed analysis of the convergence that incorporates this cost-aware constraints while optimising the objective functions. We demonstrate our algorithm based on synthetic and real-world problems in hyperparameter tuning of neural networks and random forests.

cs.LG↗