Constant Stepsize Q-learning: Distributional Convergence, Bias and Extrapolation

Stochastic Approximation (SA) is a widely used algorithmic approach in various fields, including optimization and reinforcement learning (RL). Among RL algorithms, Q-learning is particularly popular due to its empirical success. In this paper, we study asynchronous Q-learning with constant stepsize, which is commonly used in practice for its fast convergence. By connecting the constant stepsize Q-learning to a time-homogeneous Markov chain, we show the distributional convergence of the iterates in Wasserstein distance and establish its exponential convergence rate. We also establish a Central Limit Theory for Q-learning iterates, demonstrating the asymptotic normality of the averaged iterates. Moreover, we provide an explicit expansion of the asymptotic bias of the averaged iterate in stepsize. Specifically, the bias is proportional to the stepsize up to higher-order terms and we provide an explicit expression for the linear coefficient. This precise characterization of the bias allows the application of Richardson-Romberg (RR) extrapolation technique to construct a new estimate that is provably closer to the optimal Q function. Numerical results corroborate our theoretical finding on the improvement of the RR extrapolation method.

Visibility into AI Agents

Increased delegation of commercial, scientific, governmental, and personal activities to AI agents -- systems capable of pursuing complex goals with limited supervision -- may exacerbate existing societal risks and introduce new risks. Understanding and mitigating these risks involves critically evaluating existing governance structures, revising and adapting these structures where needed, and ensuring accountability of key stakeholders. Information about where, why, how, and by whom certain AI agents are used, which we refer to as visibility, is critical to these objectives. In this paper, we assess three categories of measures to increase visibility into AI agents: agent identifiers, real-time monitoring, and activity logging. For each, we outline potential implementations that vary in intrusiveness and informativeness. We analyze how the measures apply across a spectrum of centralized through decentralized deployment contexts, accounting for various actors in the supply chain including hardware and software service providers. Finally, we discuss the implications of our measures for privacy and concentration of power. Further work into understanding the measures and mitigating their negative impacts can help to build a foundation for the governance of AI agents.

Inconsistency Masks: Removing the Uncertainty from Input-Pseudo-Label Pairs

Generating sufficient labeled data is a significant hurdle in the efficient execution of deep learning projects, especially in uncharted territories of image segmentation where labeling demands extensive time, unlike classification tasks. Our study confronts this challenge, operating in an environment constrained by limited hardware resources and the lack of extensive datasets or pre-trained models. We introduce the novel use of Inconsistency Masks (IM) to effectively filter uncertainty in image-pseudo-label pairs, substantially elevating segmentation quality beyond traditional semi-supervised learning techniques. By integrating IM with other methods, we demonstrate remarkable binary segmentation performance on the ISIC 2018 dataset, starting with just 10% labeled data. Notably, three of our hybrid models outperform those trained on the fully labeled dataset. Our approach consistently achieves exceptional results across three additional datasets and shows further improvement when combined with other techniques. For comprehensive and robust evaluation, this paper includes an extensive analysis of prevalent semi-supervised learning strategies, all trained under identical starting conditions. The full code is available at: https://github.com/MichaelVorndran/InconsistencyMasks

Towards a Systems Theory of Algorithms

Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization, wherein {\em in vivo} algorithms interact with their environment. Examples of such {\em open} include various real-time optimization-based control strategies, reinforcement learning, decision-making architectures, online optimization, and many more. Further, even {\em closed} algorithms in learning or optimization are increasingly abstracted in block diagrams with interacting dynamic modules and pipelines. In this opinion paper, we state our vision on a to-be-cultivated {\em systems theory of algorithms} and argue in favour of viewing algorithms as open dynamical systems interacting with other algorithms, physical systems, humans, or databases. Remarkably, the manifold tools developed under the umbrella of systems theory also provide valuable insights into this burgeoning paradigm shift and its accompanying challenges in the algorithmic world. We survey various instances where the principles of algorithmic systems theory are being developed and outline pertinent modeling, analysis, and design challenges.

TPRF: A Transformer-based Pseudo-Relevance Feedback Model for Efficient and Effective Retrieval

This paper considers Pseudo-Relevance Feedback (PRF) methods for dense retrievers in a resource constrained environment such as that of cheap cloud instances or embedded systems (e.g., smartphones and smartwatches), where memory and CPU are limited and GPUs are not present. For this, we propose a transformer-based PRF method (TPRF), which has a much smaller memory footprint and faster inference time compared to other deep language models that employ PRF mechanisms, with a marginal effectiveness loss. TPRF learns how to effectively combine the relevance feedback signals from dense passage representations. Specifically, TPRF provides a mechanism for modelling relationships and weights between the query and the relevance feedback signals. The method is agnostic to the specific dense representation used and thus can be generally applied to any dense retriever.

Deep Non-Parametric Time Series Forecaster

This paper presents non-parametric baseline models for time series forecasting. Unlike classical forecasting models, the proposed approach does not assume any parametric form for the predictive distribution and instead generates predictions by sampling from the empirical distribution according to a tunable strategy. By virtue of this, the model is always able to produce reasonable forecasts (i.e., predictions within the observed data range) without fail unlike classical models that suffer from numerical stability on some data distributions. Moreover, we develop a global version of the proposed method that automatically learns the sampling strategy by exploiting the information across multiple related time series. The empirical evaluation shows that the proposed methods have reasonable and consistent performance across all datasets, proving them to be strong baselines to be considered in one's forecasting toolbox.

Machine learning approach to detect dynamical states from recurrence measures

We integrate machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series. We implement three machine learning algorithms Logistic Regression, Random Forest, and Support Vector Machine for this study. The input features are derived from the recurrence quantification of nonlinear time series and characteristic measures of the corresponding recurrence networks. For training and testing we generate synthetic data from standard nonlinear dynamical systems and evaluate the efficiency and performance of the machine learning algorithms in classifying time series into periodic, chaotic, hyper-chaotic, or noisy categories. Additionally, we explore the significance of input features in the classification scheme and find that the features quantifying the density of recurrence points are the most relevant. Furthermore, we illustrate how the trained algorithms can successfully predict the dynamical states of two variable stars, SX Her and AC Her from the data of their light curves.

An Exploratory Study of Multimodal Physiological Data in Jazz Improvisation Using Basic Machine Learning Techniques

Our study delves into the "Embodied Musicking Dataset," exploring the intertwined relationships and correlations between physiological and psychological dimensions during improvisational music performances. The primary objective is to ascertain the presence of a definitive causal or correlational relationship between these states and comprehend their manifestation in musical compositions. This rich dataset provides a perspective on how musicians coordinate their physicality with sonic events in real-time improvisational scenarios, emphasizing the concept of "Embodied Musicking."

Weakly supervised covariance matrices alignment through Stiefel matrices estimation for MEG applications

This paper introduces a novel domain adaptation technique for time series data, called Mixing model Stiefel Adaptation (MSA), specifically addressing the challenge of limited labeled signals in the target dataset. Leveraging a domain-dependent mixing model and the optimal transport domain adaptation assumption, we exploit abundant unlabeled data in the target domain to ensure effective prediction by establishing pairwise correspondence with equivalent signal variances between domains. Theoretical foundations are laid for identifying crucial Stiefel matrices, essential for recovering underlying signal variances from a Riemannian representation of observed signal covariances. We propose an integrated cost function that simultaneously learns these matrices, pairwise domain relationships, and a predictor, classifier, or regressor, depending on the task. Applied to neuroscience problems, MSA outperforms recent methods in brain-age regression with task variations using magnetoencephalography (MEG) signals from the Cam-CAN dataset.

DALex: Lexicase-like Selection via Diverse Aggregation

Lexicase selection has been shown to provide advantages over other selection algorithms in several areas of evolutionary computation and machine learning. In its standard form, lexicase selection filters a population or other collection based on randomly ordered training cases that are considered one at a time. This iterated filtering process can be time-consuming, particularly in settings with large numbers of training cases. In this paper, we propose a new method that is nearly equivalent to lexicase selection in terms of the individuals that it selects, but which does so significantly more quickly. The new method, called DALex (for Diversely Aggregated Lexicase), selects the best individual with respect to a weighted sum of training case errors, where the weights are randomly sampled. This allows us to formulate the core computation required for selection as matrix multiplication instead of recursive loops of comparisons, which in turn allows us to take advantage of optimized and parallel algorithms designed for matrix multiplication for speedup. Furthermore, we show that we can interpolate between the behavior of lexicase selection and its "relaxed" variants, such as epsilon or batch lexicase selection, by adjusting a single hyperparameter, named "particularity pressure," which represents the importance granted to each individual training case. Results on program synthesis, deep learning, symbolic regression, and learning classifier systems demonstrate that DALex achieves significant speedups over lexicase selection and its relaxed variants while maintaining almost identical problem-solving performance. Under a fixed computational budget, these savings free up resources that can be directed towards increasing population size or the number of generations, enabling the potential for solving more difficult problems.