This paper studies offline policy learning, which aims at utilizing observations collected a priori (from either fixed or adaptively evolving behavior policies) to learn an optimal individualized decision rule that achieves the best overall outcomes for a given population. Existing policy learning methods rely on a uniform overlap assumption, i.e., the propensities of exploring all actions for all individual characteristics must be lower bounded. As one has no control over the data collection process, this assumption can be unrealistic in many situations, especially when the behavior policies are allowed to evolve over time with diminishing propensities for certain actions. In this paper, we propose Pessimistic Policy Learning (PPL), a new algorithm that optimizes lower confidence bounds (LCBs) -- instead of point estimates -- of the policy values. The LCBs are constructed using knowledge of the behavior policies for collecting the offline data. Without assuming any uniform overlap condition, we establish a data-dependent upper bound for the suboptimality of our algorithm, which only depends on (i) the overlap for the optimal policy, and (ii) the complexity of the policy class we optimize over. As an implication, for adaptively collected data, we ensure efficient policy learning as long as the propensities for optimal actions are lower bounded over time, while those for suboptimal ones are allowed to diminish arbitrarily fast. In our theoretical analysis, we develop a new self-normalized type concentration inequality for inverse-propensity-weighting estimators, generalizing the well-known empirical Bernstein's inequality to unbounded and non-i.i.d. data. We complement our theory with an efficient optimization algorithm via Majorization-Minimization and policy tree search, as well as extensive simulation studies and real-world applications that demonstrate the efficacy of PPL.
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In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols, both in sample and computational complexity, for the task of inferring the parameters of their underlying quadratic Hamiltonian under the assumption of bounded temperature, squeezing, displacement and maximal degree of the interaction graph. Our protocol only requires heterodyne measurements, which are often experimentally feasible, and has a sample complexity that scales logarithmically with the number of modes. Furthermore, we show that it is possible to learn the underlying interaction graph in a similar setting and sample complexity. Taken together, our results put the status of the quantum Hamiltonian learning problem for continuous variable systems in a much more advanced state when compared to spins, where state-of-the-art results are either unavailable or quantitatively inferior to ours. In addition, we use our techniques to obtain the first results on learning Gaussian states in trace distance with a quadratic scaling in precision and polynomial in the number of modes, albeit imposing certain restrictions on the Gaussian states. Our main technical innovations are several continuity bounds for the covariance and Hamiltonian matrix of a Gaussian state, which are of independent interest, combined with what we call the local inversion technique. In essence, the local inversion technique allows us to reliably infer the Hamiltonian of a Gaussian state by only estimating in parallel submatrices of the covariance matrix whose size scales with the desired precision, but not the number of modes. This way we bypass the need to obtain precise global estimates of the covariance matrix, controlling the sample complexity.
Recent advances in artificial intelligence (AI) have produced systems capable of increasingly sophisticated performance on cognitive tasks. However, AI systems still struggle in critical ways: unpredictable and novel environments (robustness), lack of transparency in their reasoning (explainability), challenges in communication and commitment (cooperation), and risks due to potential harmful actions (safety). We argue that these shortcomings stem from one overarching failure: AI systems lack wisdom. Drawing from cognitive and social sciences, we define wisdom as the ability to navigate intractable problems - those that are ambiguous, radically uncertain, novel, chaotic, or computationally explosive - through effective task-level and metacognitive strategies. While AI research has focused on task-level strategies, metacognition - the ability to reflect on and regulate one's thought processes - is underdeveloped in AI systems. In humans, metacognitive strategies such as recognizing the limits of one's knowledge, considering diverse perspectives, and adapting to context are essential for wise decision-making. We propose that integrating metacognitive capabilities into AI systems is crucial for enhancing their robustness, explainability, cooperation, and safety. By focusing on developing wise AI, we suggest an alternative to aligning AI with specific human values - a task fraught with conceptual and practical difficulties. Instead, wise AI systems can thoughtfully navigate complex situations, account for diverse human values, and avoid harmful actions. We discuss potential approaches to building wise AI, including benchmarking metacognitive abilities and training AI systems to employ wise reasoning. Prioritizing metacognition in AI research will lead to systems that act not only intelligently but also wisely in complex, real-world situations.
Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The LA is exact if the function is proportional to a normal density; its effectiveness therefore depends on the function's true shape. Here, we propose the use of the probabilistic numerical framework to develop a diagnostic for the LA and its underlying shape assumptions, modelling the function and its integral as a Gaussian process and devising a "test" by conditioning on a finite number of function values. The test is decidedly non-asymptotic and is not intended as a full substitute for numerical integration - rather, it is simply intended to test the feasibility of the assumptions underpinning the LA with as minimal computation. We discuss approaches to optimize and design the test, apply it to known sample functions, and highlight the challenges of high dimensions.
This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic equations of index 2. The proposed methods iteratively construct a probability distribution over the solution of deterministic problems, enhancing the information obtained from the numerical simulation. Within this paper, we examine the efficacy of the randomized versions of the implicit Euler method, the midpoint scheme, and exponential integrators of first and second order. By demonstrating the consistency and convergence properties of these solvers, we illustrate their utility in capturing the sensitivity of the solution to numerical errors. Our analysis establishes the theoretical validity of randomized time integration for constrained systems and offers insights into the calibration of probabilistic integrators for practical applications.
Methods for analyzing representations in neural systems are increasingly popular tools in neuroscience and mechanistic interpretability. Measures comparing neural activations across conditions, architectures, and species give scalable ways to understand information transformation within different neural networks. However, recent findings show that some metrics respond to spurious signals, leading to misleading results. Establishing benchmark test cases is thus essential for identifying the most reliable metric and potential improvements. We propose that compositional learning in recurrent neural networks (RNNs) can provide a test case for dynamical representation alignment metrics. Implementing this case allows us to evaluate if metrics can identify representations that develop throughout learning and determine if representations identified by metrics reflect the network's actual computations. Building both attractor and RNN based test cases, we show that the recently proposed Dynamical Similarity Analysis (DSA) is more noise robust and reliably identifies behaviorally relevant representations compared to prior metrics (Procrustes, CKA). We also demonstrate how such test cases can extend beyond metric evaluation to study new architectures. Specifically, testing DSA in modern (Mamba) state space models suggests that these models, unlike RNNs, may not require changes in recurrent dynamics due to their expressive hidden states. Overall, we develop test cases that showcase how DSA's enhanced ability to detect dynamical motifs makes it highly effective for identifying ongoing computations in RNNs and revealing how networks learn tasks.
This dissertation studies a fundamental open challenge in deep learning theory: why do deep networks generalize well even while being overparameterized, unregularized and fitting the training data to zero error? In the first part of the thesis, we will empirically study how training deep networks via stochastic gradient descent implicitly controls the networks' capacity. Subsequently, to show how this leads to better generalization, we will derive {\em data-dependent} {\em uniform-convergence-based} generalization bounds with improved dependencies on the parameter count. Uniform convergence has in fact been the most widely used tool in deep learning literature, thanks to its simplicity and generality. Given its popularity, in this thesis, we will also take a step back to identify the fundamental limits of uniform convergence as a tool to explain generalization. In particular, we will show that in some example overparameterized settings, {\em any} uniform convergence bound will provide only a vacuous generalization bound. With this realization in mind, in the last part of the thesis, we will change course and introduce an {\em empirical} technique to estimate generalization using unlabeled data. Our technique does not rely on any notion of uniform-convergece-based complexity and is remarkably precise. We will theoretically show why our technique enjoys such precision. We will conclude by discussing how future work could explore novel ways to incorporate distributional assumptions in generalization bounds (such as in the form of unlabeled data) and explore other tools to derive bounds, perhaps by modifying uniform convergence or by developing completely new tools altogether.
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.
Deep learning constitutes a recent, modern technique for image processing and data analysis, with promising results and large potential. As deep learning has been successfully applied in various domains, it has recently entered also the domain of agriculture. In this paper, we perform a survey of 40 research efforts that employ deep learning techniques, applied to various agricultural and food production challenges. We examine the particular agricultural problems under study, the specific models and frameworks employed, the sources, nature and pre-processing of data used, and the overall performance achieved according to the metrics used at each work under study. Moreover, we study comparisons of deep learning with other existing popular techniques, in respect to differences in classification or regression performance. Our findings indicate that deep learning provides high accuracy, outperforming existing commonly used image processing techniques.
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