Contextual Bandits for Resource-Constrained Devices using Probabilistic Learning

Contextual bandits (CB) are online sequential decision-making problems under partial feedback that underpin many adaptive services. There is a growing demand to deploy CB agents directly on-device, under strict constraints on memory, compute, and energy. However, standard linear CB algorithms are often impractical for resource-constrained devices with their unfavorable scaling in computational and memory costs. Recently, HD-CB, a CB approach based on hyperdimensional computing principles, has been proposed to model and solve CB problems by moving into high-dimensional spaces. HD-CB offers faster convergence, favorable scalability, and improves memory efficiency compared to linear CB algorithms. However, its learning rule is accumulation-based: the values of action vectors grow over time, requiring high precision. While periodic binarization can prevent overflow in low-precision components, it may discard important information about magnitudes and degrade decision quality. This paper introduces probabilistic HD-CB, a low-precision variant that replaces deterministic accumulation with a probabilistic update rule. At each step, only a random subset of vector components is updated, with a time-decaying update probability, and component values are constrained to a predefined range [-k,+k]. This approach enables low-precision components, prevents overflow without periodic binarization, and reduces the expected update cost in proportion to the fraction of updated components. Off-policy evaluation on standardized synthetic CB benchmarks using the Open Bandit Pipeline shows that probabilistic HD-CB consistently outperforms binarized HD-CB at equal precision, while approaching the performance of HD-CB with as few as 3 bits per component.

Efficient Hyperdimensional Computing with Modular Composite Representations

The modular composite representation (MCR) is a computing model that represents information with high-dimensional integer vectors using modular arithmetic. Originally proposed as a generalization of the binary spatter code model, it aims to provide higher representational power while remaining a lighter alternative to models requiring high-precision components. Despite this potential, MCR has received limited attention. Systematic analyses of its trade-offs and comparisons with other models are lacking, sustaining the perception that its added complexity outweighs the improved expressivity. In this work, we revisit MCR by presenting its first extensive evaluation, demonstrating that it achieves a unique balance of capacity, accuracy, and hardware efficiency. Experiments measuring capacity demonstrate that MCR outperforms binary and integer vectors while approaching complex-valued representations at a fraction of their memory footprint. Evaluation on 123 datasets confirms consistent accuracy gains and shows that MCR can match the performance of binary spatter codes using up to 4x less memory. We investigate the hardware realization of MCR by showing that it maps naturally to digital logic and by designing the first dedicated accelerator. Evaluations on basic operations and 7 selected datasets demonstrate a speedup of up to 3 orders of magnitude and significant energy reductions compared to software implementation. When matched for accuracy against binary spatter codes, MCR achieves on average 3.08x faster execution and 2.68x lower energy consumption. These findings demonstrate that, although MCR requires more sophisticated operations than binary spatter codes, its modular arithmetic and higher per-component precision enable lower dimensionality. When realized with dedicated hardware, this results in a faster, more energy-efficient, and high-precision alternative to existing models.

HD-CB: The First Exploration of Hyperdimensional Computing for Contextual Bandits Problems

Hyperdimensional Computing (HDC), also known as Vector Symbolic Architectures, is a computing paradigm that combines the strengths of symbolic reasoning with the efficiency and scalability of distributed connectionist models in artificial intelligence. HDC has recently emerged as a promising alternative for performing learning tasks in resource-constrained environments thanks to its energy and computational efficiency, inherent parallelism, and resilience to noise and hardware faults. This work introduces the Hyperdimensional Contextual Bandits (HD-CB): the first exploration of HDC to model and automate sequential decision-making Contextual Bandits (CB) problems. The proposed approach maps environmental states in a high-dimensional space and represents each action with dedicated hypervectors (HVs). At each iteration, these HVs are used to select the optimal action for the given context and are updated based on the received reward, replacing computationally expensive ridge regression procedures required by traditional linear CB algorithms with simple, highly parallel vector operations. We propose four HD-CB variants, demonstrating their flexibility in implementing different exploration strategies, as well as techniques to reduce memory overhead and the number of hyperparameters. Extensive simulations on synthetic datasets and a real-world benchmark reveal that HD-CB consistently achieves competitive or superior performance compared to traditional linear CB algorithms, while offering faster convergence time, lower computational complexity, improved scalability, and high parallelism.