Whittle Index Learning Algorithms for Restless Bandits with Constant Stepsizes

We study the Whittle index learning algorithm for restless multi-armed bandits. We consider index learning algorithm with Q-learning. We first present Q-learning algorithm with exploration policies -- epsilon-greedy, softmax, epsilon-softmax with constant stepsizes. We extend the study of Q-learning to index learning for single-armed restless bandit. The algorithm of index learning is two-timescale variant of stochastic approximation, on slower timescale we update index learning scheme and on faster timescale we update Q-learning assuming fixed index value. In Q-learning updates are in asynchronous manner. We study constant stepsizes two timescale stochastic approximation algorithm. We provide analysis of two-timescale stochastic approximation for index learning with constant stepsizes. Further, we present study on index learning with deep Q-network (DQN) learning and linear function approximation with state-aggregation method. We describe the performance of our algorithms using numerical examples. We have shown that index learning with Q learning, DQN and function approximations learns the Whittle index.

A Prototype Model of Zero-Trust Architecture Blockchain with EigenTrust-Based Practical Byzantine Fault Tolerance Protocol to Manage Decentralized Clinical Trials

The COVID-19 pandemic necessitated the emergence of decentralized Clinical Trials (DCTs) due to patient retention, accelerate trials, improve data accessibility, enable virtual care, and facilitate seamless communication through integrated systems. However, integrating systems in DCTs exposes clinical data to potential security threats, making them susceptible to theft at any stage, a high risk of protocol deviations, and monitoring issues. To mitigate these challenges, blockchain technology serves as a secure framework, acting as a decentralized ledger, creating an immutable environment by establishing a zero-trust architecture, where data are deemed untrusted until verified. In combination with Internet of Things (IoT)-enabled wearable devices, blockchain secures the transfer of clinical trial data on private blockchains during DCT automation and operations. This paper proposes a prototype model of the Zero-Trust Architecture Blockchain (z-TAB) to integrate patient-generated clinical trial data during DCT operation management. The EigenTrust-based Practical Byzantine Fault Tolerance (T-PBFT) algorithm has been incorporated as a consensus protocol, leveraging Hyperledger Fabric. Furthermore, the Internet of Things (IoT) has been integrated to streamline data processing among stakeholders within the blockchain platforms. Rigorous evaluation has been done to evaluate the quality of the system.

Indexability of Finite State Restless Multi-Armed Bandit and Rollout Policy

We consider finite state restless multi-armed bandit problem. The decision maker can act on M bandits out of N bandits in each time step. The play of arm (active arm) yields state dependent rewards based on action and when the arm is not played, it also provides rewards based on the state and action. The objective of the decision maker is to maximize the infinite horizon discounted reward. The classical approach to restless bandits is Whittle index policy. In such policy, the M arms with highest indices are played at each time step. Here, one decouples the restless bandits problem by analyzing relaxed constrained restless bandits problem. Then by Lagrangian relaxation problem, one decouples restless bandits problem into N single-armed restless bandit problems. We analyze the single-armed restless bandit. In order to study the Whittle index policy, we show structural results on the single armed bandit model. We define indexability and show indexability in special cases. We propose an alternative approach to verify the indexable criteria for a single armed bandit model using value iteration algorithm. We demonstrate the performance of our algorithm with different examples. We provide insight on condition of indexability of restless bandits using different structural assumptions on transition probability and reward matrices. We also study online rollout policy and discuss the computation complexity of algorithm and compare that with complexity of index computation. Numerical examples illustrate that index policy and rollout policy performs better than myopic policy.