Fee estimation for light-clients (Part 2)

By Riccardo Casatta on 1/26/2021 - Tags: Fee, Machine learning

This post is part 2 of 3 of a series. (Part 1, Part 3)

# The dataset

The dataset (opens new window) is publicly available (~500MB gzip compressed, ~2GB as plain CSV).

The output of the model is the fee rate, expressed in [satoshi/vbytes].

What about the inputs? Generally speaking, we have two main requirements for what can be included as input for our model:

  • It must be correlated to the output, even with a non-linear relation.
  • It must be available to a light client: for instance, assuming to have knowledge and an index of the last 1000 blocks is considered too much.

To evaluate the approach we are taking, we also want to compare our model's results with another available estimation: for this reason the dataset includes data to compute the error agains Bitcoin Core's estimatesmartfee results, even though we are not going to use it for this model.

The dataset will contain only transactions that spend already confirmed inputs. If we wanted to include transactions with unconfirmed inputs as well, the fee rate would have to be computed as a whole; for example if transaction t2 spends an unconfirmed input from t1 (while t1 only spends confirmed inputs, and all its other outputs are unspent), the aggregated fee rate would have to be used. Supposing f() is extracts the absolute fee and w() the transaction weight, the aggregated fee rate would be (f(t1) + f(t2)) / (w(t1) + w(t2)). Thus, as already said previously, to keep things simple the model simply discards all the transaction that would need to perform this computation.

For the same reason the dataset has the parent_in_cpfp flag. When a transaction has inputs confirmed (so it's not excluded by the previous rule) but one or more of its output have been spent by a transaction confirmed in the same block, parent_in_cpfp is 1. Transactions with parent_in_cpfp = 1 are included in the dataset but excluded by the current model, since the miner probably considered an aggregated fee rate while picking the transactions to build a block.

# The mempool

The most important input of our model is the current status of the mempool itself. However, we cannot feed the model with a list of the fee rate of every unconfirmed transaction, because this array would have a variable length. To overcome this, the transaction contained in the mempool are grouped in "buckets" which are basically subsets of the mempool where all the transactions contained in a bucket have a similar fee rate. In particular we only care about the number of transaction in every bucket, not which transactions it contains.

The mempool buckets array is defined by two parameters, the percentage_increment and the array_max value. Starting from the minimum fee rate value min_relay_fee=1.0, the ith element is: a_i=min_relay_fee * (1+percentage_increment)^(i+1)

For instance, choosing the mempool buckets array to have parameters percentage_increment = 50% and array_max = 500.0 sat/vbytes the buckets would be constructed like so:

bucket bucket min fee rate bucket max fee rate
a_0 1.0 1.5
a_1 1.5 2.25
a_2 2.25 3.375
a_15 437.89 inf

The array stops at a15 because a16 would have a bucket min greater than array_max.

The model is for light-client such as neutrino (opens new window) based ones. In these clients the mempool is already available (it's needed to check for received transactions) but we can't compute fee rates of this transactions because previous confirmed inputs are not in the mempool!

Luckily, thanks to temporal locality [1], an important part of mempool transactions spend outputs created very recently, for example in the last 6 blocks. The blocks are available through the p2p network, and downloading the last 6 is considered a good compromise between resource consumption and accurate prediction. We need the model to be built with the same data available in the prediction phase, as a consequence the mempool data in the dataset refers only to transactions having their inputs in the last 6 blocks. However the bitcoin-csv tool inside the data logger (opens new window) allows to configure this parameter.

# The outliers

The dataset also contains the block percentile fee rate q_k, considering r_i to be the rate of the ith transaction in a block, q_k is the fee rate value such that for each transaction in a block r_i < q_k returns the k% transactions in the block that are paying lower fees.

Percentiles are not used to feed the model but to filter some outliers tx. Removing this observations is controversial at best and considered cheating at worse. However, it should be considered that Bitcoin Core estimatesmartfee doesn't even bother to give estimation for the next block, we think this is due to the fact that many transactions that are confirming in the next block are huge overestimation, or clearly errors like this one (opens new window) we found when we started logging data. These outliers are several for transactions confirming in the next block (confirms_in=1), less so for confirms_in=2, mostly disappeared for confirms_in=3 or more. It's counterintuitive that overestimation exists for confirms_in>1, by definition an overestimation is a fee rate way higher than needed, so how is possible that an overestimation doesn't enter the very next block? There are a couple of reasons why a block is discovered without containing a transaction with high fee rate:

  • network latency: my node saw the transaction but the miner didn't see that transaction yet,
  • block building latency: the miner saw the transaction, but didn't finish to rebuild the block template or decided it's more efficient to finish a cycle on the older block template.

To keep the model balanced, when overestimation is filtered out, underestimation are filtered out as well. This also has the effect to remove some of the transactions possibly included because a fee is payed out-of-band. Another reason to filter transactions is that the dataset is over-represented by transactions with low confirms_in: more than 50% of transactions get confirmed in the next block, so we think it's good to filter some of these transactions.

The applied filters are the following:

confirms_in lower higher
1 q45 q55
2 q30 q70
3 q1 q99

Not yet convinced by the removal of these outliers? The dataset (opens new window) contains all the observations, make your model 😃

# Recap

column used in the model description
txid no Transaction hash, useful for debugging
timestamp converted The time when the transaction has been added in the mempool, in the model is used in the form day_of_week and hour
current_height no The blockchain height seen by the node in this moment
confirms_in yes This transaction confirmed at block height current_height+confirms_in
fee_rate target This transaction fee rate measured in [sat/vbytes]
fee_rate_bytes no fee rate in satoshi / bytes, used to check Bitcoin Core estimatesmartfee predictions
block_avg_fee no block average fee rate [sat/vbytes] of block current_height+confirms_in
core_econ no bitcoin estimatesmartfee result for confirms_in block target and in economic mode. Could be not available ? when a block is connected more recently than the estimation has been requested, estimation are requested every 10 secs.
core_cons no Same as above but with conservative mode
mempool_len no Sum of the mempool transactions with fee rate available (sum of every a* field)
parent_in_cpfp no It's 1 when the transaction has outputs that are spent in the same block in which the transaction is confirmed (they are parent in a CPFP relations).
q1-q30-... no Transaction confirming fast could be outliers, usually paying a lot more than required, this percentiles are used to filter those transactions,
a1-a2-... yes Contains the number of transaction in the mempool with known fee rate in the ith bucket.

The good, the bad and the ugly

My biological neural network fired this, I think it's because a lot of chapters start with "The"

In the previous Part 1 we talked about the problem.

In the following Part 3 we are going to talk about the model.

  1. In computer science temporal locality refers to the tendency to access recent data more often than older data. ↩︎