Read the equation
The argmax expression denotes an input that achieves the largest utility, assuming a maximizer exists. It does not itself specify a gradient method, a step size, or a unique solution. The project scalar rule instead moves x toward the supplied utility value.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
## 3.4 Family 3: Optimization ``` f₃(x) = x + 0.2 · softsign(utility - x) ``` **Equation Type**: Gradient ascent: x* = arg max U(x) **Explanation**: Actively seeks to maximize utility by moving toward higher-value states. The larger 0.2 coefficient makes this an aggressive optimizer. The softsign prevents overshooting. ## 3.5 Family 4: Bayesian Inference ``` f₄(x) = clamp₀₁((x + utility) / (1 + |utility|)) ``` **Equation Type**: Posterior update: P(θ|D) ∝ P(D|θ)P(θ)
Exact original notation
Gradient ascent: x* = arg max U(x)