Online learning provides a strong theoretical foundation for caching, but existing algorithms often rely on idealized arbitrary-precision computations and incur per-request overheads that scale with the catalog size, making them difficult to deploy in practice. To address this limitation, we introduce quantized Online Gradient Descent (qOGD), a caching algorithm that supports heterogeneous object sizes and a broad class of caching performance metrics. qOGD builds on OGD but is inherently quantized. Quantization yields constant amortized time per request and robustness to finite-precision implementations, two properties that make it well suited to practical implementations. We establish guarantees on cache update cost and dynamic regret, and show that qOGD matches the fundamental O(CT) static-regret lower bound for caching. Experiments on real-world traces show that qOGD achieves runtimes and hit ratios comparable to those of state-of-the-art caching algorithms, while reducing cache-update costs.
We study the mean-field model of the Join-Idle-Queue (JIQ) load balancing algorithm, where the ratio r=n/m of servers to dispatchers is fixed. For the classical setting without token redundancy (d=1), we derive fully explicit expressions for the steady-state probability q0 that a dispatcher has no token and for the mean response time, as well as for the stationary queue-length distribution.For systems with redundant tokens (d≥2), we show that fully explicit solutions are no longer available, but the model admits a tractable implicit characterization. We then analyze the heavy-traffic regime and derive a general expression for the heavy-traffic prefactor of the mean response time. In the large-r limit, we establish a simple scaling law showing that the mean response time decreases as 1/(d2r), revealing a quadratic improvement due to redundancy.Our results provide new analytical insight into the performance of JIQ and its extensions, and complement existing numerical and simulation-based analyses.
