We study a sequential binary prediction setting where the forecaster is evaluated in terms of the calibration distance, which is defined as the $L_1$ distance between the predicted values and the set of predictions that are perfectly calibrated in hindsight. This is analogous to a calibration measure recently proposed by B{\l}asiok, Gopalan, Hu and Nakkiran (STOC 2023) for the offline setting. The calibration distance is a natural and intuitive measure of deviation from perfect calibration, and satisfies a Lipschitz continuity property which does not hold for many popular calibration measures, such as the $L_1$ calibration error and its variants. We prove that there is a forecasting algorithm that achieves an $O(\sqrt{T})$ calibration distance in expectation on an adversarially chosen sequence of $T$ binary outcomes. At the core of this upper bound is a structural result showing that the calibration distance is accurately approximated by the lower calibration distance, which is a continuous relaxation of the former. We then show that an $O(\sqrt{T})$ lower calibration distance can be achieved via a simple minimax argument and a reduction to online learning on a Lipschitz class. On the lower bound side, an $\Omega(T^{1/3})$ calibration distance is shown to be unavoidable, even when the adversary outputs a sequence of independent random bits, and has an additional ability to early stop (i.e., to stop producing random bits and output the same bit in the remaining steps). Interestingly, without this early stopping, the forecaster can achieve a much smaller calibration distance of $\mathrm{polylog}(T)$.
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In the field of Sequential Decision Making (SDM), two paradigms have historically vied for supremacy: Automated Planning (AP) and Reinforcement Learning (RL). In the spirit of reconciliation, this article reviews AP, RL and hybrid methods (e.g., novel learn to plan techniques) for solving Sequential Decision Processes (SDPs), focusing on their knowledge representation: symbolic, subsymbolic, or a combination. Additionally, it also covers methods for learning the SDP structure. Finally, we compare the advantages and drawbacks of the existing methods and conclude that neurosymbolic AI poses a promising approach for SDM, since it combines AP and RL with a hybrid knowledge representation.
Evaluating the generalisation capabilities of multimodal models based solely on their performance on out-of-distribution data fails to capture their true robustness. This work introduces a comprehensive evaluation framework that systematically examines the role of instructions and inputs in the generalisation abilities of such models, considering architectural design, input perturbations across language and vision modalities, and increased task complexity. The proposed framework uncovers the resilience of multimodal models to extreme instruction perturbations and their vulnerability to observational changes, raising concerns about overfitting to spurious correlations. By employing this evaluation framework on current Transformer-based multimodal models for robotic manipulation tasks, we uncover limitations and suggest future advancements should focus on architectural and training innovations that better integrate multimodal inputs, enhancing a model's generalisation prowess by prioritising sensitivity to input content over incidental correlations.
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at tackling one or more difficulty in an optimization problem. For instance, evolutionary algorithms have a niche in handling complexities like discontinuity, non-differentiability, discreteness and non-convexity. However, evolutionary algorithms may get computationally expensive for mathematically well behaved problems with large number of variables for which classical mathematical programming approaches are better suited. In this paper, we demonstrate a decomposition strategy that allows us to synergistically apply two complementary approaches at the same time on a complex optimization problem. Evolutionary algorithms are useful in this context as their flexibility makes pairing with other solution approaches easy. The decomposition idea is a special case of bilevel optimization that separates the difficulties into two levels and assigns different approaches at each level that is better equipped at handling them. We demonstrate the benefits of the proposed decomposition idea on a wide range of test problems.
Many organizations use algorithms that have a disparate impact, i.e., the benefits or harms of the algorithm fall disproportionately on certain social groups. Addressing an algorithm's disparate impact can be challenging, however, because it is often unclear whether it is possible to reduce this impact without sacrificing other objectives of the organization, such as accuracy or profit. Establishing the improvability of algorithms with respect to multiple criteria is of both conceptual and practical interest: in many settings, disparate impact that would otherwise be prohibited under US federal law is permissible if it is necessary to achieve a legitimate business interest. The question is how a policy-maker can formally substantiate, or refute, this "necessity" defense. In this paper, we provide an econometric framework for testing the hypothesis that it is possible to improve on the fairness of an algorithm without compromising on other pre-specified objectives. Our proposed test is simple to implement and can be applied under any exogenous constraint on the algorithm space. We establish the large-sample validity and consistency of our test, and illustrate its practical application by evaluating a healthcare algorithm originally considered by Obermeyer et al. (2019). In this application, we reject the null hypothesis that it is not possible to reduce the algorithm's disparate impact without compromising the accuracy of its predictions.
The aim of this study is to investigate the effectiveness of ChatGPT 3.5 in developing algorithms for data generation within the framework of Item Response Theory (IRT) using the R programming language. In this context, validity examinations were conducted on data sets generated according to the Two-Parameter Logistic Model (2PLM) with algorithms written by ChatGPT 3.5 and researchers. These examinations considered whether the data sets met the IRT assumptions and the simulation conditions of the item parameters. As a result, it was determined that while ChatGPT 3.5 was quite successful in generating data that met the IRT assumptions, it was less effective in meeting the simulation conditions of the item parameters compared to the algorithm developed by the researchers. In this regard, ChatGPT 3.5 is recommended as a useful tool that researchers can use in developing data generation algorithms for IRT.
Terrain Classification is an essential task in space exploration, where unpredictable environments are difficult to observe using only exteroceptive sensors such as vision. Implementing Neural Network classifiers can have high performance but can be deemed untrustworthy as they lack transparency, which makes them unreliable for taking high-stakes decisions during mission planning. We address this by proposing Neural Networks with Uncertainty Quantification in Terrain Classification. We enable our Neural Networks with Monte Carlo Dropout, DropConnect, and Flipout in time series-capable architectures using only proprioceptive data as input. We use Bayesian Optimization with Hyperband for efficient hyperparameter optimization to find optimal models for trustworthy terrain classification.
In the space sector, due to environmental conditions and restricted accessibility, robust fault detection methods are imperative for ensuring mission success and safeguarding valuable assets. This work proposes a novel approach leveraging Physics-Informed Real NVP neural networks, renowned for their ability to model complex and high-dimensional distributions, augmented with a self-supervised task based on sensors' data permutation. It focuses on enhancing fault detection within the satellite multivariate time series. The experiments involve various configurations, including pre-training with self-supervision, multi-task learning, and standalone self-supervised training. Results indicate significant performance improvements across all settings. In particular, employing only the self-supervised loss yields the best overall results, suggesting its efficacy in guiding the network to extract relevant features for fault detection. This study presents a promising direction for improving fault detection in space systems and warrants further exploration in other datasets and applications.
We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the dot-product self-attention, positional encoding and feed-forward layer, affect its expressive power, and we study their combined effects through establishing explicit approximation rates. Our study reveals the roles of critical parameters in the Transformer, such as the number of layers and the number of attention heads. These theoretical insights are validated experimentally and offer natural suggestions for alternative architectures.
The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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