发表机构
Ericsson（爱立信）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文区分任务导向量化两种机制，指出二次调度中应量化负载并对质心注水，而非直接量化注水动作，并推导精确Lloyd条件与功率图编码器。
AI 中文摘要
我们在已知确定性预言机动作的任务导向量化中区分两种机制。对于无约束的内部预言机和光滑强凹效用函数，通过向量Lloyd-Max对预言机动作进行量化，可最小化均方误差替代目标，并实现对最优K级任务量化器的β/α近似。该简化对于各向同性二次损失是精确的，相应的任务率失真函数被两个普通率失真函数所夹持。受预算约束的二次调度则不同：预言机满足变分不等式，因此对注水动作进行量化通常并非最优。我们推导了这种情况下的精确Lloyd型条件。量化器单元的最优动作是在该单元条件均值负载处进行注水，而最优编码器将负载空间划分为仿射功率图单元。因此，正确的做法是对负载进行量化并对其质心进行注水。当单元跨越注水活动集边界时，这一区别至关重要。
英文摘要
We distinguish two regimes in task-oriented quantization with a known deterministic oracle action. For an unconstrained interior oracle and a smooth strongly concave utility, quantizing the oracle action by vector Lloyd-Max minimizes a mean-squared-error surrogate and achieves a $β/α$ approximation to the optimal $K$-level task quantizer. The reduction is exact for isotropic quadratic loss, and the corresponding task rate--distortion function is bracketed by two ordinary rate--distortion functions. Budget-constrained quadratic scheduling is different: the oracle satisfies a variational inequality, so quantizing water-filled actions is not generally optimal. We derive the exact Lloyd-type conditions for this case. The optimal action for a quantizer cell is water-filling evaluated at the cell's conditional-mean load, and the optimal encoder partitions load space into affine power-diagram cells. Thus the correct prescription is to quantize the load and water-fill its centroid. The distinction is material whenever a cell crosses water-filling active-set boundaries.
