Svalues

Svalues are a class of scalar measures assigned to elements of a domain in order to quantify their desirability, relevance, or stakes under a specified criterion. They are used to compare alternatives, guide decision making, and support evaluation and optimization in a range of theoretical and practical settings.

Formally, let S be a set of states or outcomes. An Svalue function s: S -> R maps each element to a real number, representing its relative quality. Svalues may derive from utilities, costs, rewards, or probabilistic assessments, and they are frequently normalized to a common range.

In dynamic contexts such as decision processes, Svalues can be defined as value functions that summarize future potential. For example, under a policy pi and discount factor gamma, V_pi(s) = E[ sum_{t=0}^∞ gamma^t u(s_t) | s0 = s ]. Other implementations may compute static Svalues from data without temporal structure.

Variants of Svalues include time-dependent S_t(s) to capture change over time, and multi-criteria Svalues obtained by scalarizing several criteria through a weighting function. Some formulations require additivity along transitions, while others rely on maximum principles or learned approximations.

Applications span reinforcement learning, resource allocation, risk assessment, and strategic planning. Svalues provide a compact summary that facilitates ranking, thresholding, and policy selection without exposing full distributions or trajectories.

Although the term Svalues appears in several theoretical discussions and niche applications, it is not a universally standardized term. In practice, related concepts such as value functions, utilities, or scores may play a similar role depending on the domain.