In this paper, we describe a novel solution to compute optimal warehouse allocations for fashion inventory. Procured inventory must be optimally allocated to warehouses in proportion to the regional demand around the warehouse. This will ensure that demand is fulfilled by the nearest warehouse thereby minimizing the delivery logistics cost and delivery times. These are key metrics to drive profitability and customer experience respectively. Warehouses have capacity constraints and allocations must minimize inter warehouse redistribution cost of the inventory. This leads to maximum Regional Utilization (RU). We use machine learning and optimization methods to build an efficient solution to this warehouse allocation problem. We use machine learning models to estimate the geographical split of the demand for every product. We use Integer Programming methods to compute the optimal feasible warehouse allocations considering the capacity constraints. We conduct a back-testing by using this solution and validate the efficiency of this model by demonstrating a significant uptick in two key metrics Regional Utilization (RU) and Percentage Two-day-delivery (2DD). We use this process to intelligently create purchase orders with warehouse assignments for Myntra, a leading online fashion retailer.

Traditional methods for black box optimization require a considerable number of evaluations which can be time consuming, unpractical, and often unfeasible for many engineering applications that rely on accurate representations and expensive models to evaluate. Bayesian Optimization (BO) methods search for the global optimum by progressively (actively) learning a surrogate model of the objective function along the search path. Bayesian optimization can be accelerated through multifidelity approaches which leverage multiple black-box approximations of the objective functions that can be computationally cheaper to evaluate, but still provide relevant information to the search task. Further computational benefits are offered by the availability of parallel and distributed computing architectures whose optimal usage is an open opportunity within the context of active learning. This paper introduces the Resource Aware Active Learning (RAAL) strategy, a multifidelity Bayesian scheme to accelerate the optimization of black box functions. At each optimization step, the RAAL procedure computes the set of best sample locations and the associated fidelity sources that maximize the information gain to acquire during the parallel/distributed evaluation of the objective function, while accounting for the limited computational budget. The scheme is demonstrated for a variety of benchmark problems and results are discussed for both single fidelity and multifidelity settings. In particular we observe that the RAAL strategy optimally seeds multiple points at each iteration allowing for a major speed up of the optimization task.

Lagrangian methods are widely used algorithms for constrained optimization problems, but their learning dynamics exhibit oscillations and overshoot which, when applied to safe reinforcement learning, leads to constraint-violating behavior during agent training. We address this shortcoming by proposing a novel Lagrange multiplier update method that utilizes derivatives of the constraint function. We take a controls perspective, wherein the traditional Lagrange multiplier update behaves as \emph{integral} control; our terms introduce \emph{proportional} and \emph{derivative} control, achieving favorable learning dynamics through damping and predictive measures. We apply our PID Lagrangian methods in deep RL, setting a new state of the art in Safety Gym, a safe RL benchmark. Lastly, we introduce a new method to ease controller tuning by providing invariance to the relative numerical scales of reward and cost. Our extensive experiments demonstrate improved performance and hyperparameter robustness, while our algorithms remain nearly as simple to derive and implement as the traditional Lagrangian approach.

Linear models have shown great effectiveness and flexibility in many fields such as machine learning, signal processing and statistics. They can represent rich spaces of functions while preserving the convexity of the optimization problems where they are used, and are simple to evaluate, differentiate and integrate. However, for modeling non-negative functions, which are crucial for unsupervised learning, density estimation, or non-parametric Bayesian methods, linear models are not applicable directly. Moreover, current state-of-the-art models like generalized linear models either lead to non-convex optimization problems, or cannot be easily integrated. In this paper we provide the first model for non-negative functions which benefits from the same good properties of linear models. In particular, we prove that it admits a representer theorem and provide an efficient dual formulation for convex problems. We study its representation power, showing that the resulting space of functions is strictly richer than that of generalized linear models. Finally we extend the model and the theoretical results to functions with outputs in convex cones. The paper is complemented by an experimental evaluation of the model showing its effectiveness in terms of formulation, algorithmic derivation and practical results on the problems of density estimation, regression with heteroscedastic errors, and multiple quantile regression.

This paper investigates reinforcement learning with constraints, which is indispensable in safety-critical environments. To drive the constraint violation monotonically decrease, the constraints are taken as Lyapunov functions, and new linear constraints are imposed on the updating dynamics of the policy parameters such that the original safety set is forward-invariant in expectation. As the new guaranteed-feasible constraints are imposed on the updating dynamics instead of the original policy parameters, classic optimization algorithms are no longer applicable. To address this, we propose to learn a neural network-based meta-optimizer to optimize the objective while satisfying such linear constraints. The constraint-satisfaction is achieved via projection onto a polytope formulated by multiple linear inequality constraints, which can be solved analytically with our newly designed metric. Ultimately, the meta-optimizer trains the policy network to monotonically decrease the constraint violation and maximize the cumulative reward. Numerical results validate the theoretical findings.

As robots become ubiquitous in the workforce, it is essential that human-robot collaboration be both intuitive and adaptive. A robot's quality improves based on its ability to explicitly reason about the time-varying (i.e. learning curves) and stochastic capabilities of its human counterparts, and adjust the joint workload to improve efficiency while factoring human preferences. We introduce a novel resource coordination algorithm that enables robots to explore the relative strengths and learning abilities of their human teammates, by constructing schedules that are robust to stochastic and time-varying human task performance. We first validate our algorithmic approach using data we collected from a user study (n = 20), showing we can quickly generate and evaluate a robust schedule while discovering the latest individual worker proficiency. Second, we conduct a between-subjects experiment (n = 90) to validate the efficacy of our coordinating algorithm. Results from the human-subjects experiment indicate that scheduling strategies favoring exploration tend to be beneficial for human-robot collaboration as it improves team fluency (p = 0.0438), while also maximizing team efficiency (p < 0.001).

In this paper, we develop fast algorithms for two stochastic submodular maximization problems. We start with the well-studied adaptive submodular maximization problem subject to a cardinality constraint. We develop the first linear-time algorithm which achieves a $(1-1/e-\epsilon)$ approximation ratio. Notably, the time complexity of our algorithm is $O(n\log\frac{1}{\epsilon})$ (number of function evaluations) which is independent of the cardinality constraint, where $n$ is the size of the ground set. Then we introduce the concept of fully adaptive submodularity, and develop a linear-time algorithm for maximizing a fully adaptive submoudular function subject to a partition matroid constraint. We show that our algorithm achieves a $\frac{1-1/e-\epsilon}{4-2/e-2\epsilon}$ approximation ratio using only $O(n\log\frac{1}{\epsilon})$ number of function evaluations.

Automated Machine Learning, which supports practitioners and researchers with the tedious task of manually designing machine learning pipelines, has recently achieved substantial success. In this paper we introduce new Automated Machine Learning (AutoML) techniques motivated by our winning submission to the second ChaLearn AutoML challenge, PoSH Auto-sklearn. For this, we extend Auto-sklearn with a new, simpler meta-learning technique, improve its way of handling iterative algorithms and enhance it with a successful bandit strategy for budget allocation. Furthermore, we go one step further and study the design space of AutoML itself and propose a solution towards truly hand-free AutoML. Together, these changes give rise to the next generation of our AutoML system, Auto-sklearn (2.0). We verify the improvement by these additions in a large experimental study on 39 AutoML benchmark datasets and conclude the paper by comparing to Auto-sklearn (1.0), reducing the regret by up to a factor of five.

In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is typically NP-hard, and thus alternative approximate methods should be considered. In this paper, our choice for alternative method is sparse Bayesian learning, which, as empirical Bayesian approaches, uses a parameterized prior to encourage sparsity in solution, rather than the other methods with fixed priors such as LASSO. Screening test, however, aims at quickly identifying a subset of features whose coefficients are guaranteed to be zero in the optimal solution, and then can be safely removed from the complete dictionary to obtain a smaller, more easily solved problem. Next, we solve the smaller problem, after which the solution of the original problem can be recovered by padding the smaller solution with zeros. The performance of the proposed method will be examined on various data sets and applications.

Differentially private SGD (DP-SGD) is one of the most popular methods for solving differentially private empirical risk minimization (ERM). Due to its noisy perturbation on each gradient update, the error rate of DP-SGD scales with the ambient dimension $p$, the number of parameters in the model. Such dependence can be problematic for over-parameterized models where $p \gg n$, the number of training samples. Existing lower bounds on private ERM show that such dependence on $p$ is inevitable in the worst case. In this paper, we circumvent the dependence on the ambient dimension by leveraging a low-dimensional structure of gradient space in deep networks---that is, the stochastic gradients for deep nets usually stay in a low dimensional subspace in the training process. We propose Projected DP-SGD that performs noise reduction by projecting the noisy gradients to a low-dimensional subspace, which is given by the top gradient eigenspace on a small public dataset. We provide a general sample complexity analysis on the public dataset for the gradient subspace identification problem and demonstrate that under certain low-dimensional assumptions the public sample complexity only grows logarithmically in $p$. Finally, we provide a theoretical analysis and empirical evaluations to show that our method can substantially improve the accuracy of DP-SGD.