Modifying price-weighted curve from exponential to a highly adjustabl…

…e inverted sigmoid curve
livepeer · Jan 9, 2024 · 4f28c58 · 4f28c58
1 parent 3f4ee24
commit 4f28c58
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Showing 3 changed files with 25 additions and 11 deletions.
diff --git a/cmd/livepeer/livepeer.go b/cmd/livepeer/livepeer.go
@@ -130,7 +130,9 @@ func parseLivepeerConfig() starter.LivepeerConfig {
 	cfg.SelectRandWeight = flag.Float64("selectRandFreq", *cfg.SelectRandWeight, "Weight of the random factor in the orchestrator selection algorithm")
 	cfg.SelectStakeWeight = flag.Float64("selectStakeWeight", *cfg.SelectStakeWeight, "Weight of the stake factor in the orchestrator selection algorithm")
 	cfg.SelectPriceWeight = flag.Float64("selectPriceWeight", *cfg.SelectPriceWeight, "Weight of the price factor in the orchestrator selection algorithm")
-	cfg.SelectPriceExpFactor = flag.Float64("selectPriceExpFactor", *cfg.SelectPriceExpFactor, "Expresses how significant a small change of price is for the selection algorithm; default 100")
+	cfg.SelectPriceExpFactorA = flag.Float64("selectPriceExpFactorA", *cfg.SelectPriceExpFactorA, "Expresses how significant a small change of price is for the selection algorithm; default 0.001")
+	cfg.SelectPriceExpFactorB = flag.Float64("selectPriceExpFactorB", *cfg.SelectPriceExpFactorB, "Expresses how significant a small change of price is for the selection algorithm; default 20")
+	cfg.SelectPriceCenter = flag.Float64("selectPriceCenter", *cfg.SelectPriceCenter, "Centers the price weighted selection curve around this number, giving increasingly diminishing returns starting at that price point; default 150")
 	cfg.OrchPerfStatsURL = flag.String("orchPerfStatsUrl", *cfg.OrchPerfStatsURL, "URL of Orchestrator Performance Stream Tester")
 	cfg.Region = flag.String("region", *cfg.Region, "Region in which a broadcaster is deployed; used to select the region while using the orchestrator's performance stats")
 	cfg.MaxPricePerUnit = flag.Int("maxPricePerUnit", *cfg.MaxPricePerUnit, "The maximum transcoding price (in wei) per 'pixelsPerUnit' a broadcaster is willing to accept. If not set explicitly, broadcaster is willing to accept ANY price")

diff --git a/cmd/livepeer/starter/starter.go b/cmd/livepeer/starter/starter.go
@@ -92,7 +92,9 @@ type LivepeerConfig struct {
 	SelectRandWeight             *float64
 	SelectStakeWeight            *float64
 	SelectPriceWeight            *float64
-	SelectPriceExpFactor         *float64
+	SelectPriceExpFactorA        *float64
+	SelectPriceExpFactorB        *float64
+	SelectPriceCenter            *float64
 	OrchPerfStatsURL             *string
 	Region                       *string
 	MaxPricePerUnit              *int
@@ -169,7 +171,9 @@ func DefaultLivepeerConfig() LivepeerConfig {
 	defaultSelectRandWeight := 0.3
 	defaultSelectStakeWeight := 0.7
 	defaultSelectPriceWeight := 0.0
-	defaultSelectPriceExpFactor := 100.0
+	defaultSelectPriceExpFactorA := 0.001
+	defaultSelectPriceExpFactorB := 20.0
+	defaultSelectPriceCenter := 150.0
 	defaultMaxSessions := strconv.Itoa(10)
 	defaultOrchPerfStatsURL := ""
 	defaultRegion := ""
@@ -257,7 +261,9 @@ func DefaultLivepeerConfig() LivepeerConfig {
 		SelectRandWeight:             &defaultSelectRandWeight,
 		SelectStakeWeight:            &defaultSelectStakeWeight,
 		SelectPriceWeight:            &defaultSelectPriceWeight,
-		SelectPriceExpFactor:         &defaultSelectPriceExpFactor,
+		SelectPriceExpFactorA:        &defaultSelectPriceExpFactorA,
+		SelectPriceExpFactorB:        &defaultSelectPriceExpFactorB,
+		SelectPriceCenter:            &defaultSelectPriceCenter,
 		MaxSessions:                  &defaultMaxSessions,
 		OrchPerfStatsURL:             &defaultOrchPerfStatsURL,
 		Region:                       &defaultRegion,
@@ -1498,11 +1504,13 @@ func createSelectionAlgorithm(cfg LivepeerConfig) (common.SelectionAlgorithm, er
 			*cfg.SelectStakeWeight, *cfg.SelectPriceWeight, *cfg.SelectRandWeight)
 	}
 	return server.ProbabilitySelectionAlgorithm{
-		MinPerfScore:   *cfg.MinPerfScore,
-		StakeWeight:    *cfg.SelectStakeWeight,
-		PriceWeight:    *cfg.SelectPriceWeight,
-		RandWeight:     *cfg.SelectRandWeight,
-		PriceExpFactor: *cfg.SelectPriceExpFactor,
+		MinPerfScore:    *cfg.MinPerfScore,
+		StakeWeight:     *cfg.SelectStakeWeight,
+		PriceWeight:     *cfg.SelectPriceWeight,
+		RandWeight:      *cfg.SelectRandWeight,
+		PriceExpFactorA: *cfg.SelectPriceExpFactorA,
+		PriceExpFactorB: *cfg.SelectPriceExpFactorB,
+		PriceCenter:     *cfg.SelectPriceCenter,
 	}, nil
 }
 

diff --git a/server/selection_algorithm.go b/server/selection_algorithm.go
@@ -17,7 +17,9 @@ type ProbabilitySelectionAlgorithm struct {
 	PriceWeight float64
 	RandWeight  float64
 
-	PriceExpFactor float64
+	PriceExpFactorA float64
+	PriceExpFactorB float64
+	PriceCenter     float64
 }
 
 func (sa ProbabilitySelectionAlgorithm) Select(addrs []ethcommon.Address, stakes map[ethcommon.Address]int64, prices map[ethcommon.Address]float64, perfScores map[ethcommon.Address]float64) ethcommon.Address {
@@ -50,9 +52,11 @@ func (sa ProbabilitySelectionAlgorithm) filter(addrs []ethcommon.Address, scores
 
 func (sa ProbabilitySelectionAlgorithm) calculateProbabilities(addrs []ethcommon.Address, stakes map[ethcommon.Address]int64, prices map[ethcommon.Address]float64) map[ethcommon.Address]float64 {
 	pricesNorm := map[ethcommon.Address]float64{}
+
+	// Normalize price-weighted selection according to a inverted sigmoid function
 	for _, addr := range addrs {
 		p := prices[addr]
-		pricesNorm[addr] = math.Exp(-1 * p / sa.PriceExpFactor)
+		pricesNorm[addr] = 1 / (1 + math.Pow(math.Exp(sa.PriceExpFactorA*(p-sa.PriceCenter)), sa.PriceExpFactorB))
 	}
 
 	var priceSum, stakeSum float64