Novel Kernel Models and Exact Representor Theory for Neural Networks Beyond the Over-Parameterized Regime

This paper presents two models of neural-networks and their training applicable to neural networks of arbitrary width, depth and topology, assuming only finite-energy neural activations; and a novel representor theory for neural networks in terms of a matrix-valued kernel. The first model is exact (un-approximated) and global, casting the neural network as an elements in a reproducing kernel Banach space (RKBS); we use this model to provide tight bounds on Rademacher complexity. The second model is exact and local, casting the change in neural network function resulting from a bounded change in weights and biases (ie. a training step) in reproducing kernel Hilbert space (RKHS) in terms of a local-intrinsic neural kernel (LiNK). This local model provides insight into model adaptation through tight bounds on Rademacher complexity of network adaptation. We also prove that the neural tangent kernel (NTK) is a first-order approximation of the LiNK kernel. Finally, and noting that the LiNK does not provide a representor theory for technical reasons, we present an exact novel representor theory for layer-wise neural network training with unregularized gradient descent in terms of a local-extrinsic neural kernel (LeNK). This representor theory gives insight into the role of higher-order statistics in neural network training and the effect of kernel evolution in neural-network kernel models. Throughout the paper (a) feedforward ReLU networks and (b) residual networks (ResNet) are used as illustrative examples.

Enhanced Bayesian Optimization via Preferential Modeling of Abstract Properties

Experimental (design) optimization is a key driver in designing and discovering new products and processes. Bayesian Optimization (BO) is an effective tool for optimizing expensive and black-box experimental design processes. While Bayesian optimization is a principled data-driven approach to experimental optimization, it learns everything from scratch and could greatly benefit from the expertise of its human (domain) experts who often reason about systems at different abstraction levels using physical properties that are not necessarily directly measured (or measurable). In this paper, we propose a human-AI collaborative Bayesian framework to incorporate expert preferences about unmeasured abstract properties into the surrogate modeling to further boost the performance of BO. We provide an efficient strategy that can also handle any incorrect/misleading expert bias in preferential judgments. We discuss the convergence behavior of our proposed framework. Our experimental results involving synthetic functions and real-world datasets show the superiority of our method against the baselines.

Active Level Set Estimation for Continuous Search Space with Theoretical Guarantee

A common problem encountered in many real-world applications is level set estimation where the goal is to determine the region in the function domain where the function is above or below a given threshold. When the function is black-box and expensive to evaluate, the level sets need to be found in a minimum set of function evaluations. Existing methods often assume a discrete search space with a finite set of data points for function evaluations and estimating the level sets. When applied to a continuous search space, these methods often need to first discretize the space which leads to poor results while needing high computational time. While some methods cater for the continuous setting, they still lack a proper guarantee for theoretical convergence. To address this problem, we propose a novel algorithm that does not need any discretization and can directly work in continuous search spaces. Our method suggests points by constructing an acquisition function that is defined as a measure of confidence of the function being higher or lower than the given threshold. A theoretical analysis for the convergence of the algorithm to an accurate solution is provided. On multiple synthetic and real-world datasets, our algorithm successfully outperforms state-of-the-art methods.

Policy Learning for Off-Dynamics RL with Deficient Support

Reinforcement Learning (RL) can effectively learn complex policies. However, learning these policies often demands extensive trial-and-error interactions with the environment. In many real-world scenarios, this approach is not practical due to the high costs of data collection and safety concerns. As a result, a common strategy is to transfer a policy trained in a low-cost, rapid source simulator to a real-world target environment. However, this process poses challenges. Simulators, no matter how advanced, cannot perfectly replicate the intricacies of the real world, leading to dynamics discrepancies between the source and target environments. Past research posited that the source domain must encompass all possible target transitions, a condition we term full support. However, expecting full support is often unrealistic, especially in scenarios where significant dynamics discrepancies arise. In this paper, our emphasis shifts to addressing large dynamics mismatch adaptation. We move away from the stringent full support condition of earlier research, focusing instead on crafting an effective policy for the target domain. Our proposed approach is simple but effective. It is anchored in the central concepts of the skewing and extension of source support towards target support to mitigate support deficiencies. Through comprehensive testing on a varied set of benchmarks, our method's efficacy stands out, showcasing notable improvements over previous techniques.

PINN-BO: A Black-box Optimization Algorithm using Physics-Informed Neural Networks

Black-box optimization is a powerful approach for discovering global optima in noisy and expensive black-box functions, a problem widely encountered in real-world scenarios. Recently, there has been a growing interest in leveraging domain knowledge to enhance the efficacy of machine learning methods. Partial Differential Equations (PDEs) often provide an effective means for elucidating the fundamental principles governing the black-box functions. In this paper, we propose PINN-BO, a black-box optimization algorithm employing Physics-Informed Neural Networks that integrates the knowledge from Partial Differential Equations (PDEs) to improve the sample efficiency of the optimization. We analyze the theoretical behavior of our algorithm in terms of regret bound using advances in NTK theory and prove that the use of the PDE alongside the black-box function evaluations, PINN-BO leads to a tighter regret bound. We perform several experiments on a variety of optimization tasks and show that our algorithm is more sample-efficient compared to existing methods.

Root Cause Explanation of Outliers under Noisy Mechanisms

Identifying root causes of anomalies in causal processes is vital across disciplines. Once identified, one can isolate the root causes and implement necessary measures to restore the normal operation. Causal processes are often modelled as graphs with entities being nodes and their paths/interconnections as edge. Existing work only consider the contribution of nodes in the generative process, thus can not attribute the outlier score to the edges of the mechanism if the anomaly occurs in the connections. In this paper, we consider both individual edge and node of each mechanism when identifying the root causes. We introduce a noisy functional causal model to account for this purpose. Then, we employ Bayesian learning and inference methods to infer the noises of the nodes and edges. We then represent the functional form of a target outlier leaf as a function of the node and edge noises. Finally, we propose an efficient gradient-based attribution method to compute the anomaly attribution scores which scales linearly with the number of nodes and edges. Experiments on simulated datasets and two real-world scenario datasets show better anomaly attribution performance of the proposed method compared to the baselines. Our method scales to larger graphs with more nodes and edges.

Learn to Unlearn for Deep Neural Networks: Minimizing Unlearning Interference with Gradient Projection

Recent data-privacy laws have sparked interest in machine unlearning, which involves removing the effect of specific training samples from a learnt model as if they were never present in the original training dataset. The challenge of machine unlearning is to discard information about the ``forget'' data in the learnt model without altering the knowledge about the remaining dataset and to do so more efficiently than the naive retraining approach. To achieve this, we adopt a projected-gradient based learning method, named as Projected-Gradient Unlearning (PGU), in which the model takes steps in the orthogonal direction to the gradient subspaces deemed unimportant for the retaining dataset, so as to its knowledge is preserved. By utilizing Stochastic Gradient Descent (SGD) to update the model weights, our method can efficiently scale to any model and dataset size. We provide empirically evidence to demonstrate that our unlearning method can produce models that behave similar to models retrained from scratch across various metrics even when the training dataset is no longer accessible. Our code is available at https://github.com/hnanhtuan/projected_gradient_unlearning.

LaGR-SEQ: Language-Guided Reinforcement Learning with Sample-Efficient Querying

Large language models (LLMs) have recently demonstrated their impressive ability to provide context-aware responses via text. This ability could potentially be used to predict plausible solutions in sequential decision making tasks pertaining to pattern completion. For example, by observing a partial stack of cubes, LLMs can predict the correct sequence in which the remaining cubes should be stacked by extrapolating the observed patterns (e.g., cube sizes, colors or other attributes) in the partial stack. In this work, we introduce LaGR (Language-Guided Reinforcement learning), which uses this predictive ability of LLMs to propose solutions to tasks that have been partially completed by a primary reinforcement learning (RL) agent, in order to subsequently guide the latter's training. However, as RL training is generally not sample-efficient, deploying this approach would inherently imply that the LLM be repeatedly queried for solutions; a process that can be expensive and infeasible. To address this issue, we introduce SEQ (sample efficient querying), where we simultaneously train a secondary RL agent to decide when the LLM should be queried for solutions. Specifically, we use the quality of the solutions emanating from the LLM as the reward to train this agent. We show that our proposed framework LaGR-SEQ enables more efficient primary RL training, while simultaneously minimizing the number of queries to the LLM. We demonstrate our approach on a series of tasks and highlight the advantages of our approach, along with its limitations and potential future research directions.

Predictive Modeling through Hyper-Bayesian Optimization

Model selection is an integral problem of model based optimization techniques such as Bayesian optimization (BO). Current approaches often treat model selection as an estimation problem, to be periodically updated with observations coming from the optimization iterations. In this paper, we propose an alternative way to achieve both efficiently. Specifically, we propose a novel way of integrating model selection and BO for the single goal of reaching the function optima faster. The algorithm moves back and forth between BO in the model space and BO in the function space, where the goodness of the recommended model is captured by a score function and fed back, capturing how well the model helped convergence in the function space. The score function is derived in such a way that it neutralizes the effect of the moving nature of the BO in the function space, thus keeping the model selection problem stationary. This back and forth leads to quick convergence for both model selection and BO in the function space. In addition to improved sample efficiency, the framework outputs information about the black-box function. Convergence is proved, and experimental results show significant improvement compared to standard BO.

EMOTE: An Explainable architecture for Modelling the Other Through Empathy

We can usually assume others have goals analogous to our own. This assumption can also, at times, be applied to multi-agent games - e.g. Agent 1's attraction to green pellets is analogous to Agent 2's attraction to red pellets. This "analogy" assumption is tied closely to the cognitive process known as empathy. Inspired by empathy, we design a simple and explainable architecture to model another agent's action-value function. This involves learning an "Imagination Network" to transform the other agent's observed state in order to produce a human-interpretable "empathetic state" which, when presented to the learning agent, produces behaviours that mimic the other agent. Our approach is applicable to multi-agent scenarios consisting of a single learning agent and other (independent) agents acting according to fixed policies. This architecture is particularly beneficial for (but not limited to) algorithms using a composite value or reward function. We show our method produces better performance in multi-agent games, where it robustly estimates the other's model in different environment configurations. Additionally, we show that the empathetic states are human interpretable, and thus verifiable.