Jiabin Lin

Jiabin Lin, Xian Yeow Lee, Talukder Jubery et al.

Many physical systems have underlying safety considerations that require that the strategy deployed ensures the satisfaction of a set of constraints. Further, often we have only partial information on the state of the system. We study the problem of safe real-time decision making under uncertainty. In this paper, we formulate a conservative stochastic contextual bandit formulation for real-time decision making when an adversary chooses a distribution on the set of possible contexts and the learner is subject to certain safety/performance constraints. The learner observes only the context distribution and the exact context is unknown, and the goal is to develop an algorithm that selects a sequence of optimal actions to maximize the cumulative reward without violating the safety constraints at any time step. By leveraging the UCB algorithm for this setting, we propose a conservative linear UCB algorithm for stochastic bandits with context distribution. We prove an upper bound on the regret of the algorithm and show that it can be decomposed into three terms: (i) an upper bound for the regret of the standard linear UCB algorithm, (ii) a constant term (independent of time horizon) that accounts for the loss of being conservative in order to satisfy the safety constraint, and (ii) a constant term (independent of time horizon) that accounts for the loss for the contexts being unknown and only the distribution being known. To validate the performance of our approach we perform extensive simulations on synthetic data and on real-world maize data collected through the Genomes to Fields (G2F) initiative.

Jiabin Lin, Shana Moothedath

We consider the problem where M agents collaboratively interact with an instance of a stochastic K-armed contextual bandit, where K>>M. The goal of the agents is to simultaneously minimize the cumulative regret over all the agents over a time horizon T. We consider a setting where the exact context is observed after a delay and at the time of choosing the action the agents are unaware of the context and only a distribution on the set of contexts is available. Such a situation arises in different applications where at the time of the decision the context needs to be predicted (e.g., weather forecasting or stock market prediction), and the context can be estimated once the reward is obtained. We propose an Upper Confidence Bound (UCB)-based distributed algorithm and prove the regret and communications bounds for linearly parametrized reward functions. We validated the performance of our algorithm via numerical simulations on synthetic data and real-world Movielens data.

Jiabin Lin, Shana Moothedath

We study the problem of federated stochastic multi-arm contextual bandits with unknown contexts, in which M agents are faced with different bandits and collaborate to learn. The communication model consists of a central server and the agents share their estimates with the central server periodically to learn to choose optimal actions in order to minimize the total regret. We assume that the exact contexts are not observable and the agents observe only a distribution of the contexts. Such a situation arises, for instance, when the context itself is a noisy measurement or based on a prediction mechanism. Our goal is to develop a distributed and federated algorithm that facilitates collaborative learning among the agents to select a sequence of optimal actions so as to maximize the cumulative reward. By performing a feature vector transformation, we propose an elimination-based algorithm and prove the regret bound for linearly parametrized reward functions. Finally, we validated the performance of our algorithm and compared it with another baseline approach using numerical simulations on synthetic data and on the real-world movielens dataset.

Jiabin Lin, Shana Moothedath

Multi-task representation learning is an approach that learns shared latent representations across related tasks, facilitating knowledge transfer and improving sample efficiency. This paper introduces a novel approach to multi-task representation learning in linear bandits. We consider a setting with T concurrent linear bandit tasks, each with feature dimension d, that share a common latent representation of dimension r \ll min{d,T}$, capturing their underlying relatedness. We propose a new Optimism in the Face of Uncertainty Linear (OFUL) algorithm that leverages shared low-rank representations to enhance decision-making in a sample-efficient manner. Our algorithm first collects data through an exploration phase, estimates the shared model via spectral initialization, and then conducts OFUL based learning over a newly constructed confidence set. We provide theoretical guarantees for the confidence set and prove that the unknown reward vectors lie within the confidence set with high probability. We derive cumulative regret bounds and show that the proposed approach achieves \tilde{O}(\sqrt{drNT}), a significant improvement over solving the T tasks independently, resulting in a regret of \tilde{O}(dT\sqrt{N}). We performed numerical simulations to validate the performance of our algorithm for different problem sizes.

Jiabin Lin, Shana Moothedath

This paper presents the Constrained Multi-Task Representation Learning (CMTRL) framework for linear bandits. We consider T linear bandit tasks in a d dimensional space, which share a common low-dimensional representation of dimension r, where r is much smaller than the minimum of d and T. Furthermore, tasks are constrained so that only actions meeting specific safety or performance requirements are allowed, referred to as conservative (safe) bandits. We introduce a novel algorithm, Safe-Alternating projected Gradient Descent and minimization (Safe-AltGDmin), to recover a low-rank feature matrix while satisfying the given constraints. Building on this algorithm, we propose a multi-task representation learning framework for conservative linear bandits and establish theoretical guarantees for its regret and sample complexity bounds. We presented experiments and compared the performance of our algorithm with benchmark algorithms.

Jiabin Lin, Shana Moothedath

We present conservative distributed multi-task learning in stochastic linear contextual bandits with heterogeneous agents. This extends conservative linear bandits to a distributed setting where M agents tackle different but related tasks while adhering to stage-wise performance constraints. The exact context is unknown, and only a context distribution is available to the agents as in many practical applications that involve a prediction mechanism to infer context, such as stock market prediction and weather forecast. We propose a distributed upper confidence bound (UCB) algorithm, DiSC-UCB. Our algorithm constructs a pruned action set during each round to ensure the constraints are met. Additionally, it includes synchronized sharing of estimates among agents via a central server using well-structured synchronization steps. We prove the regret and communication bounds on the algorithm. We extend the problem to a setting where the agents are unaware of the baseline reward. For this setting, we provide a modified algorithm, DiSC-UCB2, and we show that the modified algorithm achieves the same regret and communication bounds. We empirically validated the performance of our algorithm on synthetic data and real-world Movielens-100K data.