We study the safe linear bandit problem, where an agent sequentially selects actions from a convex domain to maximize an unknown objective while ensuring unknown linear constraints are satisfied on a per-round basis. Existing approaches primarily rely on optimism-based methods with frequentist confidence bounds, often leading to computationally expensive action selection routines. We propose COnstrained Linear Thompson Sampling (COLTS), a sampling-based framework that efficiently balances regret minimization and constraint satisfaction by selecting actions on the basis of noisy perturbations of the estimates of the unknown objective vector and constraint matrix. We introduce three variants of COLTS, distinguished by the learner's available side information: - S-COLTS assumes access to a known safe action and ensures strict constraint enforcement by combining the COLTS approach with a rescaling towards the safe action. For $d$-dimensional actions, this yields $\tilde{O}(\sqrt{d^3 T})$ regret and zero constraint violations (or risk). - E-COLTS enforces constraints softly under Slater's condition, and attains regret and risk of $\tilde{O}(\sqrt{d^3 T})$ by combining COLTS with uniform exploration. - R-COLTS requires no side information, and ensures instance-independent regret and risk of $\tilde{O}(\sqrt{d^3 T})$ by leveraging repeated resampling. A key technical innovation is a coupled noise design, which maintains optimism while preserving computational efficiency, which is combined with a scaling based analysis technique to address the variation of the per-round feasible region induced by sampled constraint matrices. Our methods match the regret bounds of prior approaches, while significantly reducing computational costs compared to them, thus yielding a scalable and practical approach for constrained bandit linear optimization.

While the recent literature has seen a surge in the study of constrained bandit problems, all existing methods for these begin by assuming the feasibility of the underlying problem. We initiate the study of testing such feasibility assumptions, and in particular address the problem in the linear bandit setting, thus characterising the costs of feasibility testing for an unknown linear program using bandit feedback. Concretely, we test if $\exists x: Ax \ge 0$ for an unknown $A \in \mathbb{R}^{m \times d}$, by playing a sequence of actions $x_t\in \mathbb{R}^d$, and observing $Ax_t + \mathrm{noise}$ in response. By identifying the hypothesis as determining the sign of the value of a minimax game, we construct a novel test based on low-regret algorithms and a nonasymptotic law of iterated logarithms. We prove that this test is reliable, and adapts to the `signal level,' $\Gamma,$ of any instance, with mean sample costs scaling as $\widetilde{O}(d^2/\Gamma^2)$. We complement this by a minimax lower bound of $\Omega(d/\Gamma^2)$ for sample costs of reliable tests, dominating prior asymptotic lower bounds by capturing the dependence on $d$, and thus elucidating a basic insight missing in the extant literature on such problems.

In cross-domain retrieval, a model is required to identify images from the same semantic category across two visual domains. For instance, given a sketch of an object, a model needs to retrieve a real image of it from an online store's catalog. A standard approach for such a problem is learning a feature space of images where Euclidean distances reflect similarity. Even without human annotations, which may be expensive to acquire, prior methods function reasonably well using unlabeled images for training. Our problem constraint takes this further to scenarios where the two domains do not necessarily share any common categories in training data. This can occur when the two domains in question come from different versions of some biometric sensor recording identities of different people. We posit a simple solution, which is to generate synthetic data to fill in these missing category examples across domains. This, we do via category preserving translation of images from one visual domain to another. We compare approaches specifically trained for this translation for a pair of domains, as well as those that can use large-scale pre-trained text-to-image diffusion models via prompts, and find that the latter can generate better replacement synthetic data, leading to more accurate cross-domain retrieval models. Code for our work is available at https://github.com/samarth4149/SynCDR .

Human drivers can seamlessly adapt their driving decisions across geographical locations with diverse conditions and rules of the road, e.g., left vs. right-hand traffic. In contrast, existing models for autonomous driving have been thus far only deployed within restricted operational domains, i.e., without accounting for varying driving behaviors across locations or model scalability. In this work, we propose AnyD, a single geographically-aware conditional imitation learning (CIL) model that can efficiently learn from heterogeneous and globally distributed data with dynamic environmental, traffic, and social characteristics. Our key insight is to introduce a high-capacity geo-location-based channel attention mechanism that effectively adapts to local nuances while also flexibly modeling similarities among regions in a data-driven manner. By optimizing a contrastive imitation objective, our proposed approach can efficiently scale across inherently imbalanced data distributions and location-dependent events. We demonstrate the benefits of our AnyD agent across multiple datasets, cities, and scalable deployment paradigms, i.e., centralized, semi-supervised, and distributed agent training. Specifically, AnyD outperforms CIL baselines by over 14% in open-loop evaluation and 30% in closed-loop testing on CARLA.

The safe linear bandit problem (SLB) is an online approach to linear programming with unknown objective and unknown round-wise constraints, under stochastic bandit feedback of rewards and safety risks of actions. We study aggressive \emph{doubly-optimistic play} in SLBs, and their role in avoiding the strong assumptions and poor efficacy associated with extant pessimistic-optimistic solutions. We first elucidate an inherent hardness in SLBs due the lack of knowledge of constraints: there exist `easy' instances, for which suboptimal extreme points have large `gaps', but on which SLB methods must still incur $\Omega(\sqrt{T})$ regret and safety violations due to an inability to refine the location of optimal actions to arbitrary precision. In a positive direction, we propose and analyse a doubly-optimistic confidence-bound based strategy for the safe linear bandit problem, DOSLB, which exploits supreme optimism by using optimistic estimates of both reward and safety risks to select actions. Using a novel dual analysis, we show that despite the lack of knowledge of constraints, DOSLB rarely takes overly risky actions, and obtains tight instance-dependent $O(\log^2 T)$ bounds on both efficacy regret and net safety violations up to any finite precision, thus yielding large efficacy gains at a small safety cost and without strong assumptions. Concretely, we argue that algorithm activates noisy versions of an `optimal' set of constraints at each round, and activation of suboptimal sets of constraints is limited by the larger of a safety and efficacy gap we define.

We propose a novel supervised learning approach for political ideology prediction (PIP) that is capable of predicting out-of-distribution inputs. This problem is motivated by the fact that manual data-labeling is expensive, while self-reported labels are often scarce and exhibit significant selection bias. We propose a novel statistical model that decomposes the document embeddings into a linear superposition of two vectors; a latent neutral \emph{context} vector independent of ideology, and a latent \emph{position} vector aligned with ideology. We train an end-to-end model that has intermediate contextual and positional vectors as outputs. At deployment time, our model predicts labels for input documents by exclusively leveraging the predicted positional vectors. On two benchmark datasets we show that our model is capable of outputting predictions even when trained with as little as 5\% biased data, and is significantly more accurate than the state-of-the-art. Through crowd-sourcing we validate the neutrality of contextual vectors, and show that context filtering results in ideological concentration, allowing for prediction on out-of-distribution examples.

We propose a new method for fine-grained few-shot recognition via deep object parsing. In our framework, an object is made up of K distinct parts and for each part, we learn a dictionary of templates, which is shared across all instances and categories. An object is parsed by estimating the locations of these K parts and a set of active templates that can reconstruct the part features. We recognize test instances by comparing its active templates and the relative geometry of its part locations against those of the presented few-shot instances. Our method is end-to-end trainable to learn part templates on-top of a convolutional backbone. To combat visual distortions such as orientation, pose and size, we learn templates at multiple scales, and at test-time parse and match instances across these scales. We show that our method is competitive with the state-of-the-art, and by virtue of parsing enjoys interpretability as well.

Motivated by applications to resource-limited and safety-critical domains, we study selective classification in the online learning model, wherein a predictor may abstain from classifying an instance. For example, this may model an adaptive decision to invoke more resources on this instance. Two salient aspects of the setting we consider are that the data may be non-realisable, due to which abstention may be a valid long-term action, and that feedback is only received when the learner abstains, which models the fact that reliable labels are only available when the resource intensive processing is invoked. Within this framework, we explore strategies that make few mistakes, while not abstaining too many times more than the best-in-hindsight error-free classifier from a given class. That is, the one that makes no mistakes, while abstaining the fewest number of times. We construct simple versioning-based schemes for any $\mu \in (0,1],$ that make most $T^\mu$ mistakes while incurring \smash{$\tilde{O}(T^{1-\mu})$} excess abstention against adaptive adversaries. We further show that this dependence on $T$ is tight, and provide illustrative experiments on realistic datasets.

Detecting abrupt changes in temporal behavior patterns is of interest in many industrial and security applications. Abrupt changes are often local and observable primarily through a well-aligned sensing action (e.g., a camera with a narrow field-of-view). Due to resource constraints, continuous monitoring of all of the sensors is impractical. We propose the bandit quickest changepoint detection framework as a means of balancing sensing cost with detection delay. In this framework, sensing actions (or sensors) are sequentially chosen, and only measurements corresponding to chosen actions are observed. We derive an information-theoretic lower bound on the detection delay for a general class of finitely parameterized probability distributions. We then propose a computationally efficient online sensing scheme, which seamlessly balances the need for exploration of different sensing options with exploitation of querying informative actions. We derive expected delay bounds for the proposed scheme and show that these bounds match our information-theoretic lower bounds at low false alarm rates, establishing optimality of the proposed method. We then perform a number of experiments on synthetic and real datasets demonstrating the efficacy of our proposed method.

We propose a novel method for selective classification (SC), a problem which allows a classifier to abstain from predicting some instances, thus trading off accuracy against coverage (the fraction of instances predicted). In contrast to prior gating or confidence-set based work, our proposed method optimises a collection of class-wise decoupled one-sided empirical risks, and is in essence a method for explicitly finding the largest decision sets for each class that have few false positives. This one-sided prediction (OSP) based relaxation yields an SC scheme that attains near-optimal coverage in the practically relevant high target accuracy regime, and further admits efficient implementation, leading to a flexible and principled method for SC. We theoretically derive generalization bounds for SC and OSP, and empirically we show that our scheme strongly outperforms state of the art methods in coverage at small error levels.