väärtusfunktsioon

Väärtusfunktsioon is an Estonian term that translates to “value function” in English. It refers to a mathematical or algorithmic mapping that assigns a numerical value to each element of a set, representing the desirability or worth of that element within a given context. Value functions are widely used in fields such as decision theory, economics, artificial intelligence, operations research, and game theory.

In decision theory, a value function captures an agent’s preferences over possible outcomes. It is often a utility function that reflects risk attitudes; for example, a risk‑neutral agent may assign linear values, while a risk‑averse agent might use a concave function. The function guides the agent’s choice by allowing comparison of alternative actions based on expected value. In dynamic programming, the Bellman equation uses a value function to solve optimal control problems by iterating on state‑value estimates until convergence.

In economics, value functions formalize consumer satisfaction, firm profit, and social welfare. They form the core of optimization problems like maximizing utility subject to a budget constraint or finding the equilibrium of a market. In auction theory, the valuation of an item by a bidder is described by a private value function, which can be common or independent.

Artificial intelligence and reinforcement learning employ state‑value functions to evaluate the long‑term reward prospects of a state, and Q‑value functions estimate the expected return of taking a specific action in a state. These functions are learned from experience using trial‑and‑error methods, thereby enabling agents to make strategic decisions in uncertain environments.

Historically, the concept of value functions has its origins in early statistical decision theory of the 1930s and 1940s, notably in the work of Sir Ronald Fisher and later in the development of Markov decision processes by Richard Bellman in the 1950s. Over time, the term has evolved into a cornerstone of quantitative analysis across diverse disciplines, providing a unified language for expressing preferences, expected outcomes, and optimality criteria.