I consider the setting where reviewers offer very noisy scores for a number of items for the selection of high-quality ones (e.g., peer review of large conference proceedings) whereas the owner of these items knows the true underlying scores but prefers not to provide this information. To address this withholding of information, in this paper, I introduce the \textit{Isotonic Mechanism}, a simple and efficient approach to improving on the imprecise raw scores by leveraging certain information that the owner is incentivized to provide. This mechanism takes as input the ranking of the items from best to worst provided by the owner, in addition to the raw scores provided by the reviewers. It reports adjusted scores for the items by solving a convex optimization problem. Under certain conditions, I show that the owner's optimal strategy is to honestly report the true ranking of the items to her best knowledge in order to maximize the expected utility. Moreover, I prove that the adjusted scores provided by this owner-assisted mechanism are indeed significantly more accurate than the raw scores provided by the reviewers. This paper concludes with several extensions of the Isotonic Mechanism and some refinements of the mechanism for practical considerations.

Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data, i.e. a function that is the maximum eigenvalue of an affine matrix expression of the input. This method represents a significant generalization of polyhedral (also called max-affine) regression, in which a polyhedral function (a maximum of a fixed number of affine functions) is fit to the data. We prove bounds on how well spectrahedral functions can approximate arbitrary convex functions via statistical risk analysis. We also analyze an alternating minimization algorithm for the non-convex optimization problem of fitting the best spectrahedral function to a given data set. We show that this algorithm converges geometrically with high probability to a small ball around the optimal parameter given a good initialization. Finally, we demonstrate the utility of our approach with experiments on synthetic data sets as well as real data arising in applications such as economics and engineering design.

In this paper, we consider the problem of iterative machine teaching, where a teacher provides examples sequentially based on the current iterative learner. In contrast to previous methods that have to scan over the entire pool and select teaching examples from it in each iteration, we propose a label synthesis teaching framework where the teacher randomly selects input teaching examples (e.g., images) and then synthesizes suitable outputs (e.g., labels) for them. We show that this framework can avoid costly example selection while still provably achieving exponential teachability. We propose multiple novel teaching algorithms in this framework. Finally, we empirically demonstrate the value of our framework.

Active learning is a subfield of machine learning that is devised for design and modeling of systems with highly expensive sampling costs. Industrial and engineering systems are generally subject to physics constraints that may induce fatal failures when they are violated, while such constraints are frequently underestimated in active learning. In this paper, we develop a novel active learning method that avoids failures considering implicit physics constraints that govern the system. The proposed approach is driven by two tasks: the safe variance reduction explores the safe region to reduce the variance of the target model, and the safe region expansion aims to extend the explorable region exploiting the probabilistic model of constraints. The global acquisition function is devised to judiciously optimize acquisition functions of two tasks, and its theoretical properties are provided. The proposed method is applied to the composite fuselage assembly process with consideration of material failure using the Tsai-wu criterion, and it is able to achieve zero-failure without the knowledge of explicit failure regions.

Fairness and robustness are critical elements of Trustworthy AI that need to be addressed together. Fairness is about learning an unbiased model while robustness is about learning from corrupted data, and it is known that addressing only one of them may have an adverse affect on the other. In this work, we propose a sample selection-based algorithm for fair and robust training. To this end, we formulate a combinatorial optimization problem for the unbiased selection of samples in the presence of data corruption. Observing that solving this optimization problem is strongly NP-hard, we propose a greedy algorithm that is efficient and effective in practice. Experiments show that our algorithm obtains fairness and robustness that are better than or comparable to the state-of-the-art technique, both on synthetic and benchmark real datasets. Moreover, unlike other fair and robust training baselines, our algorithm can be used by only modifying the sampling step in batch selection without changing the training algorithm or leveraging additional clean data.

The field of transportation and logistics has witnessed fundamental transformations in the last decade, due to the convergence of seemingly unrelated technologies. The fast pace of innovations has been particularly striking for an industry that had been relatively stagnant for a long time. Taxi services were born in England where a public coach service for hire was first documented in 1605. The Hackney Carriage Act, which legalized horse-drawn carriages for hire, was passed in Parliament in 1635, and a similar service was started in Paris in 1637. Public transit was invented by Blaise Pascal in 1662 through a service known as the "carriage," which was quite popular and operated for 15 years.

The goal of multi-task learning is to enable more efficient learning than single task learning by sharing model structures for a diverse set of tasks. A standard multi-task learning objective is to minimize the average loss across all tasks. While straightforward, using this objective often results in much worse final performance for each task than learning them independently. A major challenge in optimizing a multi-task model is the conflicting gradients, where gradients of different task objectives are not well aligned so that following the average gradient direction can be detrimental to specific tasks' performance. Previous work has proposed several heuristics to manipulate the task gradients for mitigating this problem. But most of them lack convergence guarantee and/or could converge to any Pareto-stationary point. In this paper, we introduce Conflict-Averse Gradient descent (CAGrad) which minimizes the average loss function, while leveraging the worst local improvement of individual tasks to regularize the algorithm trajectory. CAGrad balances the objectives automatically and still provably converges to a minimum over the average loss. It includes the regular gradient descent (GD) and the multiple gradient descent algorithm (MGDA) in the multi-objective optimization (MOO) literature as special cases. On a series of challenging multi-task supervised learning and reinforcement learning tasks, CAGrad achieves improved performance over prior state-of-the-art multi-objective gradient manipulation methods.

We consider a selection problem where sequentially arrived applicants apply for a limited number of positions/jobs. At each time step, a decision maker accepts or rejects the given applicant using a pre-trained supervised learning model until all the vacant positions are filled. In this paper, we discuss whether the fairness notions (e.g., equal opportunity, statistical parity, etc.) that are commonly used in classification problems are suitable for the sequential selection problems. In particular, we show that even with a pre-trained model that satisfies the common fairness notions, the selection outcomes may still be biased against certain demographic groups. This observation implies that the fairness notions used in classification problems are not suitable for a selection problem where the applicants compete for a limited number of positions. We introduce a new fairness notion, ``Equal Selection (ES),'' suitable for sequential selection problems and propose a post-processing approach to satisfy the ES fairness notion. We also consider a setting where the applicants have privacy concerns, and the decision maker only has access to the noisy version of sensitive attributes. In this setting, we can show that the perfect ES fairness can still be attained under certain conditions.

Goal-directed generation, aiming for solving downstream tasks by generating diverse data, has a potentially wide range of applications in the real world. Previous works tend to formulate goal-directed generation as a purely data-driven problem, which directly searches or approximates the distribution of samples satisfying the goal. However, the generation ability of preexisting work is heavily restricted by inefficient sampling, especially for sparse goals that rarely show up in off-the-shelf datasets. For instance, generating safety-critical traffic scenes with the goal of increasing the risk of collision is critical to evaluate autonomous vehicles, but the rareness of such scenes is the biggest resistance. In this paper, we integrate causality as a prior into the safety-critical scene generation process and propose a flow-based generative framework - Causal Autoregressive Flow (CausalAF). CausalAF encourages the generative model to uncover and follow the causal relationship among generated objects via novel causal masking operations instead of searching the sample only from observational data. By learning the cause-and-effect mechanism of how the generated scene achieves the goal rather than just learning correlations from data, CausalAF significantly improves the learning efficiency. Extensive experiments on three heterogeneous traffic scenes illustrate that CausalAF requires much fewer optimization resources to effectively generate goal-directed scenes for safety evaluation tasks.

Selective rationalization explains the prediction of complex neural networks by finding a small subset of the input that is sufficient to predict the neural model output. The selection mechanism is commonly integrated into the model itself by specifying a two-component cascaded system consisting of a rationale generator, which makes a binary selection of the input features (which is the rationale), and a predictor, which predicts the output based only on the selected features. The components are trained jointly to optimize prediction performance. In this paper, we reveal a major problem with such cooperative rationalization paradigm -- model interlocking. Interlocking arises when the predictor overfits to the features selected by the generator thus reinforcing the generator's selection even if the selected rationales are sub-optimal. The fundamental cause of the interlocking problem is that the rationalization objective to be minimized is concave with respect to the generator's selection policy. We propose a new rationalization framework, called A2R, which introduces a third component into the architecture, a predictor driven by soft attention as opposed to selection. The generator now realizes both soft and hard attention over the features and these are fed into the two different predictors. While the generator still seeks to support the original predictor performance, it also minimizes a gap between the two predictors. As we will show theoretically, since the attention-based predictor exhibits a better convexity property, A2R can overcome the concavity barrier. Our experiments on two synthetic benchmarks and two real datasets demonstrate that A2R can significantly alleviate the interlock problem and find explanations that better align with human judgments. We release our code at https://github.com/Gorov/Understanding_Interlocking.