37a4edbaff
I don't know why the go people thought this was a good idea, because this automatic reformatting is bound to do the wrong thing sometimes, which is very annoying. But I don't see a way to turn it off, so best to get this change out of the way. Change-Id: Ib5dbbca6a6f6fc944d76c9b511b8c904f796e4f3
68 lines
2.4 KiB
Go
68 lines
2.4 KiB
Go
// Copyright (C) 2022 Storj Labs, Inc.
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// See LICENSE for copying information.
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package reputation
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import "math"
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// UpdateReputation uses the Beta distribution model to determine a node's reputation.
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// lambda is the "forgetting factor" which determines how much past info is kept when determining current reputation score.
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// w is the normalization weight that affects how severely new updates affect the current reputation distribution.
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func UpdateReputation(isSuccess bool, alpha, beta, lambda, w float64) (newAlpha, newBeta float64) {
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// v is a single feedback value that allows us to update both alpha and beta
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var v float64 = -1
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if isSuccess {
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v = 1
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}
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newAlpha = lambda*alpha + w*(1+v)/2
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newBeta = lambda*beta + w*(1-v)/2
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return newAlpha, newBeta
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}
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// UpdateReputationMultiple works like UpdateReputation, but applies multiple
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// successive counts of an event type to the alpha and beta measures.
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//
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// With the arguments as named, applies 'count' successful audits. To apply negative
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// audits, swap the alpha and beta parameters and return values.
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//
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// WARNING: GREEK LETTER MATH AHEAD
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//
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// Applying n successful audit results to an initial alpha value of α₀ gives a
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// new α₁ value of:
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//
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// α₁ = λⁿα₀ + λⁿ⁻¹w + λⁿ⁻²w + ... + λ²w + λw + w
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//
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// The terms with w are the first n terms of a geometric series with coefficient
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// w and common ratio λ. The closed form formula for the sum of those first n
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// terms is (w(1-λⁿ) / (1-λ))
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// (https://en.wikipedia.org/wiki/Geometric_series#Closed-form_formula).
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// Adding the initial λⁿα₀ term, we get
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//
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// α₁ = λⁿα₀ + w(1-λⁿ) / (1-λ)
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//
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// The formula has the same structure for beta for n _failures_.
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//
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// β₁ = λⁿβ₀ + w(1-λⁿ) / (1-λ)
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//
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// For n _failures_,
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//
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// α₁ = λⁿα₀
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//
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// For n _successes_,
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//
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// β₁ = λⁿβ₀
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func UpdateReputationMultiple(count int, alpha, beta, lambda, w float64) (newAlpha, newBeta float64) {
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if lambda == 1 {
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// special case: when the coefficient is 1, the closed-form formula is invalid
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// (gives NaN because of a division by zero). Fortunately, the replacement
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// formula in this case is even simpler.
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newAlpha = alpha + w*float64(count)
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newBeta = beta
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} else {
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lambdaPowN := math.Pow(lambda, float64(count))
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newAlpha = lambdaPowN*alpha + w*(1-lambdaPowN)/(1-lambda)
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newBeta = lambdaPowN * beta
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}
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return newAlpha, newBeta
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}
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