From 6390036381af77fc8afbf7ef58e0163c2605f988 Mon Sep 17 00:00:00 2001 From: Michael Sutton Date: Fri, 15 Nov 2024 09:01:58 +0000 Subject: [PATCH 1/4] Track the average transaction mass throughout the mempool's lifespan using a decaying formulae --- mining/src/mempool/model/frontier.rs | 28 ++++++++++++++++++++-------- 1 file changed, 20 insertions(+), 8 deletions(-) diff --git a/mining/src/mempool/model/frontier.rs b/mining/src/mempool/model/frontier.rs index 8d2195327..c631e5c5e 100644 --- a/mining/src/mempool/model/frontier.rs +++ b/mining/src/mempool/model/frontier.rs @@ -25,20 +25,30 @@ const COLLISION_FACTOR: u64 = 4; /// hard limit in order to allow the SequenceSelector to compensate for consensus rejections. const MASS_LIMIT_FACTOR: f64 = 1.2; -/// A rough estimation for the average transaction mass. The usage is a non-important edge case -/// hence we just throw this here (as oppose to performing an accurate estimation) -const TYPICAL_TX_MASS: f64 = 2000.0; +/// Initial estimation of the average transaction mass. +const INITIAL_AVG_MASS: f64 = 2036.0; + +/// Decay factor of average mass weighting. +const AVG_MASS_DECAY_FACTOR: f64 = 0.99999; /// Management of the transaction pool frontier, that is, the set of transactions in /// the transaction pool which have no mempool ancestors and are essentially ready /// to enter the next block template. -#[derive(Default)] pub struct Frontier { /// Frontier transactions sorted by feerate order and searchable for weight sampling search_tree: SearchTree, /// Total masses: Σ_{tx in frontier} tx.mass total_mass: u64, + + /// Tracks the average transaction mass throughout the mempool's lifespan using a decayed weighting mechanism + average_transaction_mass: f64, +} + +impl Default for Frontier { + fn default() -> Self { + Self { search_tree: Default::default(), total_mass: Default::default(), average_transaction_mass: INITIAL_AVG_MASS } + } } impl Frontier { @@ -62,6 +72,11 @@ impl Frontier { let mass = key.mass; if self.search_tree.insert(key) { self.total_mass += mass; + // A decaying average formula. Denote ɛ = 1 - AVG_MASS_DECAY_FACTOR. A transaction inserted N slots ago has + // ɛ * (1 - ɛ)^N weight within the updated average. This gives some weight to the full mempool history while + // giving growing importance to more recent samples. + self.average_transaction_mass = + self.average_transaction_mass * AVG_MASS_DECAY_FACTOR + mass as f64 * (1.0 - AVG_MASS_DECAY_FACTOR); true } else { false @@ -210,10 +225,7 @@ impl Frontier { /// Builds a feerate estimator based on internal state of the ready transactions frontier pub fn build_feerate_estimator(&self, args: FeerateEstimatorArgs) -> FeerateEstimator { - let average_transaction_mass = match self.len() { - 0 => TYPICAL_TX_MASS, - n => self.total_mass() as f64 / n as f64, - }; + let average_transaction_mass = self.average_transaction_mass; let bps = args.network_blocks_per_second as f64; let mut mass_per_block = args.maximum_mass_per_block as f64; let mut inclusion_interval = average_transaction_mass / (mass_per_block * bps); From 49d2fa66b28c37df9cf34c51bc511e7e5169f159 Mon Sep 17 00:00:00 2001 From: Michael Sutton Date: Fri, 15 Nov 2024 12:32:34 +0000 Subject: [PATCH 2/4] notebook analysis --- mining/src/feerate/fee_estimation.ipynb | 128 +++++++++++++++++++++++- 1 file changed, 123 insertions(+), 5 deletions(-) diff --git a/mining/src/feerate/fee_estimation.ipynb b/mining/src/feerate/fee_estimation.ipynb index a8b8fbfc8..73d135549 100644 --- a/mining/src/feerate/fee_estimation.ipynb +++ b/mining/src/feerate/fee_estimation.ipynb @@ -14,7 +14,7 @@ }, { "cell_type": "code", - "execution_count": 97, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -464,6 +464,124 @@ "pred" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Avg transaction mass\n", + "\n", + "We suggest a decaying weight formula for calculating the average mass throughout history, as opposed to using the avergae mass of the currently existing transactions. The followig code compares the two approaches." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "An helper function for creating a long sequence of transaction masses with periods with highly unusual mass clusters\n", + "\"\"\"\n", + "def generate_seq(N, M, X, mean_bg=2036, var_bg=100, mean_cluster=50000, var_cluster=10000):\n", + " # Step 1: Generate the background data\n", + " background_data = np.random.normal(loc=mean_bg, scale=var_bg, size=N)\n", + " \n", + " # Step 2: Generate the cluster data\n", + " cluster_data = np.random.normal(loc=mean_cluster, scale=var_cluster, size=(X, M))\n", + " \n", + " # Step 3: Flatten the cluster data to make it a 1D array\n", + " cluster_data_flat = cluster_data.flatten()\n", + "\n", + " # Step 4: Choose random positions in the sequence to insert the clusters\n", + " cluster_indices = np.random.choice(N, size=X, replace=False)\n", + " \n", + " # Step 5: Insert the clusters into the background data\n", + " data_with_clusters = background_data.copy()\n", + " for i, idx in enumerate(cluster_indices):\n", + " data_with_clusters[idx:idx+M] = cluster_data_flat[i*M:(i+1)*M]\n", + " \n", + " return data_with_clusters" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Create a long sequence of transaction masses with periods with highly unusual mass clusters\n", + "N = 500_000\n", + "seq = generate_seq(N, 50, 40)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Approach 1 - calculate the current average\n", + "R = 0.8\n", + "removals = np.random.choice([0, 1], size=N, p=[R, 1 - R])\n", + "removals[100:] = 1\n", + "j = 0\n", + "y = []\n", + "for i in range(1, N+1):\n", + " y.append(np.sum(seq[j:i])/(i-j))\n", + " if removals[i-1] == 1:\n", + " j += 1\n", + "\n", + "x = np.arange(0, N)\n", + "plt.figure()\n", + "plt.plot(x, y)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N = 5_000_000\n", + "seq = generate_seq(N, 50, 40)\n", + "# Approach 2 - calculate decaying average\n", + "D = 0.99999\n", + "j = 0\n", + "y = []\n", + "avg = 2036\n", + "for i in range(N):\n", + " avg = avg * D + seq[i] * (1 - D) \n", + " y.append(avg)\n", + "\n", + "x = np.arange(0, N)\n", + "plt.figure()\n", + "plt.plot(x, y)\n", + "plt.show()" + ] + }, { "cell_type": "code", "execution_count": null, @@ -474,9 +592,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python [conda env:gr]", + "display_name": "Python 3 (ipykernel)", "language": "python", - "name": "conda-env-gr-py" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -488,9 +606,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.10.12" } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 4 } From c9a326e5f2f95816eff3a86a14a9a8178cc2b6fb Mon Sep 17 00:00:00 2001 From: Michael Sutton Date: Sun, 17 Nov 2024 09:51:36 +0000 Subject: [PATCH 3/4] finalize notebook --- mining/src/feerate/fee_estimation.ipynb | 111 +++++++++++++++--------- 1 file changed, 71 insertions(+), 40 deletions(-) diff --git a/mining/src/feerate/fee_estimation.ipynb b/mining/src/feerate/fee_estimation.ipynb index 73d135549..51b905fa2 100644 --- a/mining/src/feerate/fee_estimation.ipynb +++ b/mining/src/feerate/fee_estimation.ipynb @@ -470,58 +470,38 @@ "source": [ "## Avg transaction mass\n", "\n", - "We suggest a decaying weight formula for calculating the average mass throughout history, as opposed to using the avergae mass of the currently existing transactions. The followig code compares the two approaches." + "We suggest a decaying weight formula for calculating the average mass throughout history, as opposed to using the average mass of the currently existing transactions. The following code compares the two approaches." ] }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "\"\"\"\n", - "An helper function for creating a long sequence of transaction masses with periods with highly unusual mass clusters\n", + "Helper function for creating a long sequence of transaction masses with periods with highly unusual mass clusters\n", + "N = sequence length\n", + "M = length of each unusual cluster\n", + "X = number of unusual clusters\n", "\"\"\"\n", - "def generate_seq(N, M, X, mean_bg=2036, var_bg=100, mean_cluster=50000, var_cluster=10000):\n", - " # Step 1: Generate the background data\n", - " background_data = np.random.normal(loc=mean_bg, scale=var_bg, size=N)\n", - " \n", - " # Step 2: Generate the cluster data\n", - " cluster_data = np.random.normal(loc=mean_cluster, scale=var_cluster, size=(X, M))\n", - " \n", - " # Step 3: Flatten the cluster data to make it a 1D array\n", - " cluster_data_flat = cluster_data.flatten()\n", - "\n", - " # Step 4: Choose random positions in the sequence to insert the clusters\n", - " cluster_indices = np.random.choice(N, size=X, replace=False)\n", - " \n", - " # Step 5: Insert the clusters into the background data\n", - " data_with_clusters = background_data.copy()\n", + "def generate_seq(N, M, X, mean=2036, var=100, mean_cluster=50000, var_cluster=10000):\n", + " seq = np.random.normal(loc=mean, scale=var, size=N)\n", + " clusters = np.random.normal(loc=mean_cluster, scale=var_cluster, size=X * M)\n", + " cluster_indices = np.random.choice(N - M, size=X, replace=False)\n", " for i, idx in enumerate(cluster_indices):\n", - " data_with_clusters[idx:idx+M] = cluster_data_flat[i*M:(i+1)*M]\n", - " \n", - " return data_with_clusters" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Create a long sequence of transaction masses with periods with highly unusual mass clusters\n", - "N = 500_000\n", - "seq = generate_seq(N, 50, 40)" + " seq[idx:idx+M] = clusters[i*M:(i+1)*M]\n", + " return seq" ] }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 68, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -531,10 +511,18 @@ } ], "source": [ + "# Create a long sequence of transaction masses with periods with highly unusual mass clusters\n", + "N = 500_000\n", + "seq = generate_seq(N, 50, 40)\n", + "\n", "# Approach 1 - calculate the current average\n", + "\n", + "# Requires a removal strategy for having a meaningful \"current\"\n", "R = 0.8\n", + "# At each time step, remove the first element with probability 1 - R\n", "removals = np.random.choice([0, 1], size=N, p=[R, 1 - R])\n", - "removals[100:] = 1\n", + "# After const steps, remove with probability 1, so that we simulate a mempool with nearly const size\n", + "removals[256:] = 1\n", "j = 0\n", "y = []\n", "for i in range(1, N+1):\n", @@ -550,12 +538,12 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 82, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -567,11 +555,10 @@ "source": [ "N = 5_000_000\n", "seq = generate_seq(N, 50, 40)\n", - "# Approach 2 - calculate decaying average\n", + "# Approach 2 - calculate a decaying average\n", "D = 0.99999\n", - "j = 0\n", "y = []\n", - "avg = 2036\n", + "avg = 2000\n", "for i in range(N):\n", " avg = avg * D + seq[i] * (1 - D) \n", " y.append(avg)\n", @@ -582,6 +569,50 @@ "plt.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Approach 1: \n", + "Clearly fails in this case and is highly influenced by the unusual clusters. \n", + "\n", + "#### Approach 2:\n", + "Learns the long term average and clusters only cause minor spikes." + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Increase the mean in the long term and see how long it takes the decaying avg to fully adjust\n", + "seq2 = np.concatenate((seq, np.repeat(4000, N // 2)))\n", + "N2 = len(seq2)\n", + "y = []\n", + "avg = 2000\n", + "for i in range(N2):\n", + " avg = avg * D + seq2[i] * (1 - D) \n", + " y.append(avg)\n", + "\n", + "x = np.arange(0, N2)\n", + "plt.figure()\n", + "plt.plot(x, y)\n", + "plt.yscale('log')\n", + "plt.show()" + ] + }, { "cell_type": "code", "execution_count": null, From 694fabf6570612193b97289ca320be6f46929396 Mon Sep 17 00:00:00 2001 From: Michael Sutton Date: Sun, 17 Nov 2024 15:06:43 +0000 Subject: [PATCH 4/4] relax feerate estimator test comparisons to avoid arbitrary CI failures --- mining/src/mempool/model/frontier.rs | 20 ++++++++++++++------ 1 file changed, 14 insertions(+), 6 deletions(-) diff --git a/mining/src/mempool/model/frontier.rs b/mining/src/mempool/model/frontier.rs index c631e5c5e..4dbea9262 100644 --- a/mining/src/mempool/model/frontier.rs +++ b/mining/src/mempool/model/frontier.rs @@ -380,8 +380,12 @@ mod tests { assert_eq!(frontier.total_mass(), frontier.search_tree.ascending_iter().map(|k| k.mass).sum::()); } + /// Epsilon used for various test comparisons + const EPS: f64 = 0.000001; + #[test] fn test_feerate_estimator() { + const MIN_FEERATE: f64 = 1.0; let mut rng = thread_rng(); let cap = 2000; let mut map = HashMap::with_capacity(cap); @@ -406,13 +410,13 @@ mod tests { let args = FeerateEstimatorArgs { network_blocks_per_second: 1, maximum_mass_per_block: 500_000 }; // We are testing that the build function actually returns and is not looping indefinitely let estimator = frontier.build_feerate_estimator(args); - let estimations = estimator.calc_estimations(1.0); + let estimations = estimator.calc_estimations(MIN_FEERATE); let buckets = estimations.ordered_buckets(); // Test for the absence of NaN, infinite or zero values in buckets for b in buckets.iter() { assert!( - b.feerate.is_normal() && b.feerate >= 1.0, + b.feerate.is_normal() && b.feerate >= MIN_FEERATE - EPS, "bucket feerate must be a finite number greater or equal to the minimum standard feerate" ); assert!( @@ -453,7 +457,7 @@ mod tests { // Test for the absence of NaN, infinite or zero values in buckets for b in buckets.iter() { assert!( - b.feerate.is_normal() && b.feerate >= MIN_FEERATE, + b.feerate.is_normal() && b.feerate >= MIN_FEERATE - EPS, "bucket feerate must be a finite number greater or equal to the minimum standard feerate" ); assert!( @@ -504,7 +508,7 @@ mod tests { // Test for the absence of NaN, infinite or zero values in buckets for b in buckets.iter() { assert!( - b.feerate.is_normal() && b.feerate >= MIN_FEERATE, + b.feerate.is_normal() && b.feerate >= MIN_FEERATE - EPS, "bucket feerate must be a finite number greater or equal to the minimum standard feerate" ); assert!( @@ -518,6 +522,7 @@ mod tests { #[test] fn test_feerate_estimator_with_less_than_block_capacity() { + const MIN_FEERATE: f64 = 1.0; let mut map = HashMap::new(); for i in 0..304 { let mass: u64 = 1650; @@ -536,13 +541,16 @@ mod tests { let args = FeerateEstimatorArgs { network_blocks_per_second: 1, maximum_mass_per_block: 500_000 }; // We are testing that the build function actually returns and is not looping indefinitely let estimator = frontier.build_feerate_estimator(args); - let estimations = estimator.calc_estimations(1.0); + let estimations = estimator.calc_estimations(MIN_FEERATE); let buckets = estimations.ordered_buckets(); // Test for the absence of NaN, infinite or zero values in buckets for b in buckets.iter() { // Expect min feerate bcs blocks are not full - assert!(b.feerate == 1.0, "bucket feerate is expected to be equal to the minimum standard feerate"); + assert!( + (b.feerate - MIN_FEERATE).abs() <= EPS, + "bucket feerate is expected to be equal to the minimum standard feerate" + ); assert!( b.estimated_seconds.is_normal() && b.estimated_seconds > 0.0 && b.estimated_seconds <= 1.0, "bucket estimated seconds must be a finite number greater than zero & less than 1.0"