Many reinforcement learning (RL) algorithms are too costly to use in practice due to the large sizes $S,A$ of the problem's state and action space. To resolve this issue, we study transfer RL with latent low rank structure. We consider the problem of transferring a latent low rank representation when the source and target MDPs have transition kernels with Tucker rank $(S, d, A)$, $(S,S, d), (d, S, A)$, or $(d, d, d)$. In each setting, we introduce the transfer-ability coefficient $\alpha$ that measures the difficulty of representational transfer. Our algorithm learns latent representations in each source MDP and then exploits the linear structure to remove the dependence on $S, A $, or $SA $ in the target MDP regret bound. We complement our positive results with information theoretic lower bounds that show our algorithms (excluding the ($d, d, d$) setting) are minimax-optimal with respect to $\alpha$.

Certified adversarial robustness of large-scale deep networks has progressed substantially after the introduction of randomized smoothing. Deep net classifiers are now provably robust in their predictions against a large class of threat models, including $\ell_1$, $\ell_2$, and $\ell_\infty$ norm-bounded attacks. Certified robustness analysis by randomized smoothing has not been performed for deep regression networks where the output variable is continuous and unbounded. In this paper, we extend the existing results for randomized smoothing into regression models using powerful tools from robust statistics, in particular, $\alpha$-trimming filter as the smoothing function. Adjusting the hyperparameter $\alpha$ achieves a smooth trade-off between desired certified robustness and utility. For the first time, we propose a benchmark for certified robust regression in visual positioning systems using the Cambridge Landmarks dataset where robustness analysis is essential for autonomous navigation of AI agents and self-driving cars.

Semi-Supervised Learning (SSL) has become a preferred paradigm in many deep learning tasks, which reduces the need for human labor. Previous studies primarily focus on effectively utilising the labelled and unlabeled data to improve performance. However, we observe that how to select samples for labelling also significantly impacts performance, particularly under extremely low-budget settings. The sample selection task in SSL has been under-explored for a long time. To fill in this gap, we propose a Representative and Diverse Sample Selection approach (RDSS). By adopting a modified Frank-Wolfe algorithm to minimise a novel criterion $\alpha$-Maximum Mean Discrepancy ($\alpha$-MMD), RDSS samples a representative and diverse subset for annotation from the unlabeled data. We demonstrate that minimizing $\alpha$-MMD enhances the generalization ability of low-budget learning. Experimental results show that RDSS consistently improves the performance of several popular SSL frameworks and outperforms the state-of-the-art sample selection approaches used in Active Learning (AL) and Semi-Supervised Active Learning (SSAL), even with constrained annotation budgets.

Federated learning (FL) allows collaborative machine learning training without sharing private data. While most FL methods assume identical data domains across clients, real-world scenarios often involve heterogeneous data domains. Federated Prototype Learning (FedPL) addresses this issue, using mean feature vectors as prototypes to enhance model generalization. However, existing FedPL methods create the same number of prototypes for each client, leading to cross-domain performance gaps and disparities for clients with varied data distributions. To mitigate cross-domain feature representation variance, we introduce FedPLVM, which establishes variance-aware dual-level prototypes clustering and employs a novel $\alpha$-sparsity prototype loss. The dual-level prototypes clustering strategy creates local clustered prototypes based on private data features, then performs global prototypes clustering to reduce communication complexity and preserve local data privacy.

Imitation learning from human feedback studies how to train well-performed imitation agents with an annotator's relative comparison of two demonstrations (one demonstration is better/worse than the other), which is usually easier to collect than the perfect expert data required by traditional imitation learning. However, in many real-world applications, it is still expensive or even impossible to provide a clear pairwise comparison between two demonstrations with similar quality. This motivates us to study the problem of imitation learning with vague feedback, where the data annotator can only distinguish the paired demonstrations correctly when their quality differs significantly, i.e., one from the expert and another from the non-expert. By modeling the underlying demonstration pool as a mixture of expert and non-expert data, we show that the expert policy distribution can be recovered when the proportion $\alpha$ of expert data is known. We also propose a mixture proportion estimation method for the unknown $\alpha$ case. Then, we integrate the recovered expert policy distribution with generative adversarial imitation learning to form an end-to-end algorithm. Experiments show that our methods outperform standard and preference-based imitation learning methods on various tasks.

Individual preference (IP) stability, introduced by Ahmadi et al. (ICML 2022), is a natural clustering objective inspired by stability and fairness constraints. A clustering is $\alpha$-IP stable if the average distance of every data point to its own cluster is at most $\alpha$ times the average distance to any other cluster. Unfortunately, determining if a dataset admits a $1$-IP stable clustering is NP-Hard. Moreover, before this work, it was unknown if an $o(n)$-IP stable clustering always exists, as the prior state of the art only guaranteed an $O(n)$-IP stable clustering. We close this gap in understanding and show that an $O(1)$-IP stable clustering always exists for general metrics, and we give an efficient algorithm which outputs such a clustering. We also introduce generalizations of IP stability beyond average distance and give efficient near optimal algorithms in the cases where we consider the maximum and minimum distances within and between clusters.

Reinforcement learning (RL) has proven highly effective in addressing complex decision-making and control tasks. However, in most traditional RL algorithms, the policy is typically parameterized as a diagonal Gaussian distribution with learned mean and variance, which constrains their capability to acquire complex policies. In response to this problem, we propose an online RL algorithm termed diffusion actor-critic with entropy regulator (DACER). This algorithm conceptualizes the reverse process of the diffusion model as a novel policy function and leverages the capability of the diffusion model to fit multimodal distributions, thereby enhancing the representational capacity of the policy. Since the distribution of the diffusion policy lacks an analytical expression, its entropy cannot be determined analytically. To mitigate this, we propose a method to estimate the entropy of the diffusion policy utilizing Gaussian mixture model. Building on the estimated entropy, we can learn a parameter $\alpha$ that modulates the degree of exploration and exploitation. Parameter $\alpha$ will be employed to adaptively regulate the variance of the added noise, which is applied to the action output by the diffusion model. Experimental trials on MuJoCo benchmarks and a multimodal task demonstrate that the DACER algorithm achieves state-of-the-art (SOTA) performance in most MuJoCo control tasks while exhibiting a stronger representational capacity of the diffusion policy.

Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation after removing low-sensitivity datapoints via subsampling. However, fast algorithms for approximating sensitivities, which we show is equivalent to approximate regression, are known for only the $\ell_2$ setting, in which they are popularly termed leverage scores. In this work, we provide the first efficient algorithms for approximating $\ell_p$ sensitivities and other summary statistics of a given matrix. In particular, for a given $n \times d$ matrix, we compute $\alpha$-approximation to its $\ell_1$ sensitivities at the cost of $n/\alpha$ sensitivity computations. For estimating the total $\ell_p$ sensitivity (i.e. the sum of $\ell_p$ sensitivities), we provide an algorithm based on importance sampling of $\ell_p$ Lewis weights, which computes a constant factor approximation at the cost of roughly $\sqrt{d}$ sensitivity computations, with no polynomial dependence on $n$. Furthermore, we estimate the maximum $\ell_1$ sensitivity up to a $\sqrt{d}$ factor in $O(d)$ sensitivity computations. We also generalize these results to $\ell_p$ norms. Lastly, we experimentally show that for a wide class of structured matrices in real-world datasets, the total sensitivity can be quickly approximated and is significantly smaller than the theoretical prediction, demonstrating that real-world datasets have on average low intrinsic effective dimensionality.

We consider learning problems where the training set consists of two types of examples: private and public. The goal is to design a learning algorithm that satisfies differential privacy only with respect to the private examples. This setting interpolates between private learning (where all examples are private) and classical learning (where all examples are public). We study the limits of learning in this setting in terms of private and public sample complexities. We show that any hypothesis class of VC-dimension $d$ can be agnostically learned up to an excess error of $\alpha$ using only (roughly) $d/\alpha$ public examples and $d/\alpha^2$ private labeled examples. This result holds even when the public examples are unlabeled. This gives a quadratic improvement over the standard $d/\alpha^2$ upper bound on the public sample complexity (where private examples can be ignored altogether if the public examples are labeled). Furthermore, we give a nearly matching lower bound, which we prove via a generic reduction from this setting to the one of private learning without public data.

This paper investigates the evaluation of learned multiagent strategies in the incomplete information setting, which plays a critical role in ranking and training of agents. Traditionally, researchers have relied on Elo ratings for this purpose, with recent works also using methods based on Nash equilibria. Unfortunately, Elo is unable to handle intransitive agent interactions, and other techniques are restricted to zero-sum, two-player settings or are limited by the fact that the Nash equilibrium is intractable to compute. Recently, a ranking method called $\alpha$-Rank, relying on a new graph-based game-theoretic solution concept, was shown to tractably apply to general games. However, evaluations based on Elo or $\alpha$-Rank typically assume noise-free game outcomes, despite the data often being collected from noisy simulations, making this assumption unrealistic in practice. This paper investigates multiagent evaluation in the incomplete information regime, involving general-sum many-player games with noisy outcomes. We derive sample complexity guarantees required to confidently rank agents in this setting. We propose adaptive algorithms for accurate ranking, provide correctness and sample complexity guarantees, then introduce a means of connecting uncertainties in noisy match outcomes to uncertainties in rankings. We evaluate the performance of these approaches in several domains, including Bernoulli games, a soccer meta-game, and Kuhn poker.