Where does return collide?

The gain or loss an investment produces over a period, expressed as a rate relative to the amount put in: a total return folds together price change and any income such as dividends, and a return is judged against the risk taken to earn it. Sharpe's 1966 Mutual Fund Performance introduced the reward-to-variability ratio, now the Sharpe ratio, which divides a portfolio's excess return by its volatility and sets out the risk-return tradeoff. The referent is a rate earned on capital over time, not the extra output from adding an input, not the cumulative reward an agent collects, and not a value a function hands back to its caller.[1]

Unit

A period's gain or loss on capital, as a percentage rate

Recovery means

Not applicable

Measured by

Computed from prices and cash flows as a rate, and adjusted for risk by dividing excess return by volatility

In production theory, the returns describe how output changes as inputs are increased: under the law of diminishing marginal returns, once a point is passed each extra unit of a single input adds less output than the unit before it, while returns to scale describe what happens to output when every input is scaled up together. Cobb and Douglas's 1928 A Theory of Production fitted a production function to output, labour, and capital and made returns to scale something that could be estimated rather than only asserted. The referent is a relationship between inputs and output, not a rate earned on money, not an agent's accumulated reward, and not a value returned by a function.[2]

Unit

The extra output from one more unit of an input, or from scaling all inputs together

Recovery means

Not applicable

Measured by

Estimated from a production function relating output to input quantities, such as the elasticity of output with respect to labour or capital

In reinforcement learning, the return is the total reward an agent accumulates from a given time step onward, usually with rewards further in the future discounted so that sooner reward counts for more: it is the quantity a value function estimates and the quantity the agent is built to maximise. Sutton and Barto's Reinforcement Learning: An Introduction (1998) defines the return as this discounted sum and makes it the target that policies and value estimates are trained toward. The referent is a sum of rewards along a trajectory, not a rate earned on capital, not the output from an input, and not a value passed back at the end of a subroutine.[3]

Unit

The discounted sum of rewards received after a given time step

Recovery means

Not applicable

Measured by

Accumulated along a trajectory as a discounted sum of rewards, and estimated in expectation by a value function