In advancing the understanding of decision-making processes, Inverse Reinforcement Learning (IRL) have proven instrumental in reconstructing animal's multiple intentions amidst complex behaviors. Given the recent development of a continuous-time multi-intention IRL framework, there has been persistent inquiry into inferring discrete time-varying rewards with IRL. To tackle the challenge, we introduce Latent (Markov) Variable Inverse Q-learning (L(M)V-IQL), a novel class of IRL algorthms tailored for accommodating discrete intrinsic reward functions. Leveraging an Expectation-Maximization approach, we cluster observed expert trajectories into distinct intentions and independently solve the IRL problem for each. Demonstrating the efficacy of L(M)V-IQL through simulated experiments and its application to different real mouse behavior datasets, our approach surpasses current benchmarks in animal behavior prediction, producing interpretable reward functions. This advancement holds promise for neuroscience and cognitive science, contributing to a deeper understanding of decision-making and uncovering underlying brain mechanisms.

Weakly supervised learning generally faces challenges in applicability to various scenarios with diverse weak supervision and in scalability due to the complexity of existing algorithms, thereby hindering the practical deployment. This paper introduces a general framework for learning from weak supervision (GLWS) with a novel algorithm. Central to GLWS is an Expectation-Maximization (EM) formulation, adeptly accommodating various weak supervision sources, including instance partial labels, aggregate statistics, pairwise observations, and unlabeled data. We further present an advanced algorithm that significantly simplifies the EM computational demands using a Non-deterministic Finite Automaton (NFA) along with a forward-backward algorithm, which effectively reduces time complexity from quadratic or factorial often required in existing solutions to linear scale. The problem of learning from arbitrary weak supervision is therefore converted to the NFA modeling of them. GLWS not only enhances the scalability of machine learning models but also demonstrates superior performance and versatility across 11 weak supervision scenarios. We hope our work paves the way for further advancements and practical deployment in this field.

Ecological rationality refers to the notion that humans are rational agents adapted to their environment. However, testing this theory remains challenging due to two reasons: the difficulty in defining what tasks are ecologically valid and building rational models for these tasks. In this work, we demonstrate that large language models can generate cognitive tasks, specifically category learning tasks, that match the statistics of real-world tasks, thereby addressing the first challenge. We tackle the second challenge by deriving rational agents adapted to these tasks using the framework of meta-learning, leading to a class of models called ecologically rational meta-learned inference (ERMI). ERMI quantitatively explains human data better than seven other cognitive models in two different experiments. It additionally matches human behavior on a qualitative level: (1) it finds the same tasks difficult that humans find difficult, (2) it becomes more reliant on an exemplar-based strategy for assigning categories with learning, and (3) it generalizes to unseen stimuli in a human-like way. Furthermore, we show that ERMI's ecologically valid priors allow it to achieve state-of-the-art performance on the OpenML-CC18 classification benchmark.

The expected loss is an upper bound to the model generalization error which admits robust PAC-Bayes bounds for learning. However, loss minimization is known to ignore misspecification, where models cannot exactly reproduce observations. This leads to significant underestimates of parameter uncertainties in the large data, or underparameterized, limit. We analyze the generalization error of near-deterministic, misspecified and underparametrized surrogate models, a regime of broad relevance in science and engineering. We show posterior distributions must cover every training point to avoid a divergent generalization error and derive an ensemble {ansatz} that respects this constraint, which for linear models incurs minimal overhead. The efficient approach is demonstrated on model problems before application to high dimensional datasets in atomistic machine learning. Parameter uncertainties from misspecification survive in the underparametrized limit, giving accurate prediction and bounding of test errors.

Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying hyperparameters - most of the theoretical literature assumes those hyperparameters are known. The commonly used maximum likelihood estimator for hyperparameters of the Gaussian process is consistent only if the data fills the space uniformly, which does not have to be the case in Bayesian optimisation. Since no guarantees exist regarding the correctness of hyperparameter estimation, and those hyperparameters can significantly affect the Gaussian process fit, theoretical analysis of Bayesian optimisation with unknown hyperparameters is very challenging. Previously proposed algorithms with the no-regret property were only able to handle the special case of unknown lengthscales, reproducing kernel Hilbert space norm and applied only to the frequentist case. We propose a novel algorithm, HE-GP-UCB, which is the first algorithm enjoying the no-regret property in the case of unknown hyperparameters of arbitrary form, and which supports both Bayesian and frequentist settings. Our proof idea is novel and can easily be extended to other variants of Bayesian optimisation. We show this by extending our algorithm to the adversarially robust optimisation setting under unknown hyperparameters. Finally, we empirically evaluate our algorithm on a set of toy problems and show that it can outperform the maximum likelihood estimator.

A major challenge in sample-based inference (SBI) for Bayesian neural networks is the size and structure of the networks' parameter space. Our work shows that successful SBI is possible by embracing the characteristic relationship between weight and function space, uncovering a systematic link between overparameterization and the difficulty of the sampling problem. Through extensive experiments, we establish practical guidelines for sampling and convergence diagnosis. As a result, we present a Bayesian deep ensemble approach as an effective solution with competitive performance and uncertainty quantification.

We introduce an Ordinary Differential Equation (ODE) based deep generative method for learning a conditional distribution, named the Conditional Follmer Flow. Starting from a standard Gaussian distribution, the proposed flow could efficiently transform it into the target conditional distribution at time 1. For effective implementation, we discretize the flow with Euler's method where we estimate the velocity field nonparametrically using a deep neural network. Furthermore, we derive a non-asymptotic convergence rate in the Wasserstein distance between the distribution of the learned samples and the target distribution, providing the first comprehensive end-to-end error analysis for conditional distribution learning via ODE flow. Our numerical experiments showcase its effectiveness across a range of scenarios, from standard nonparametric conditional density estimation problems to more intricate challenges involving image data, illustrating its superiority over various existing conditional density estimation methods.

This stochastic filtering approach is especially appealing for the control of such partially observed dynamical systems. This includes among others, e.g., control problems This work proposes a decision-making framework with noisy sensor measurements, such as grasping for partially observable systems in continuous and navigation in robotics (Kurniawati et al., 2008) or time with discrete state and action cognitive medium access control (Zhao et al., 2005) for spaces. As optimal decision-making becomes communication systems. For finding decision strategies, intractable for large state spaces we employ which use the available observational data to control approximation methods for the filtering and the system at hand, a solid framework can be found the control problem that scale well with an increasing in the area of optimal control (Stengel, 1994).

Self-supervised learning (SSL) learns representations by leveraging an auxiliary unsupervised task, such as classifying semantically related samples, e.g. different data augmentations or modalities. Of the many approaches to SSL, contrastive methods, e.g. SimCLR, CLIP and VicREG, have gained attention for learning representations that achieve downstream performance close to that of supervised learning. However, a theoretical understanding of the mechanism behind these methods eludes. We propose a generative latent variable model for the data and show that several families of discriminative self-supervised algorithms, including contrastive methods, approximately induce its latent structure over representations, providing a unifying theoretical framework. We also justify links to mutual information and the use of a projection head. Fitting our model generatively, as SimVE, improves performance over previous VAE methods on common benchmarks (e.g. FashionMNIST, CIFAR10, CelebA), narrows the gap to discriminative methods on _content_ classification and, as our analysis predicts, outperforms them where _style_ information is required, taking a step toward task-agnostic representations.

In recent years, there has been a lot of research work activity focused on carrying out asymptotic and non-asymptotic convergence analyses for two-timescale actor critic algorithms where the actor updates are performed on a timescale that is slower than that of the critic. In a recent work, the critic-actor algorithm has been presented for the infinite horizon discounted cost setting in the look-up table case where the timescales of the actor and the critic are reversed and asymptotic convergence analysis has been presented. In our work, we present the first critic-actor algorithm with function approximation and in the long-run average reward setting and present the first finite-time (non-asymptotic) analysis of such a scheme. We obtain optimal learning rates and prove that our algorithm achieves a sample complexity of $\mathcal{\tilde{O}}(\epsilon^{-2.08})$ for the mean squared error of the critic to be upper bounded by $\epsilon$ which is better than the one obtained for actor-critic in a similar setting. We also show the results of numerical experiments on three benchmark settings and observe that the critic-actor algorithm competes well with the actor-critic algorithm.