Dear René,
thank you for the great work!
One quick question regarding the consequence you mentioned: it seems
plausible that manipulating the path choices would become harder, if the
ability of doing so was correlated with the capacity locked in the
network. However, if paths were only chosen regarding the probability of
payment success (and neglecting accruing fees), couldn't high-capacity
nodes in absence of competition simply raise their fee levels
indefinitely, since they would be chosen regardless? Do you have any
ideas how to protect against this?
I imagine that some kind of 'mixed' strategy could be reasonable, in
which certain paths are pre-filtered based on the probability of payment
success, and then the final path is selected along the lines of the
currently deployed fee rate/CLTV risk assessment?
Kind Regards,
Elias
On 17 Mar 2021, at 13:50, René Pickhardt via Lightning-dev wrote:
Dear fellow Lightning Network developers,
I am very pleased to share with you some research progress [0] with
respect
to achieving better payment path finding and a better reliability of
the
payment process.
TL;DR summary: In payment (multi)path finding use the (multi)paths
with the
highest success probability instead of the shortest or cheapest ones.
(multi)path success probability is the product of channel success
probabilities. Given current data crawled on the Network the channel
success probability grows with the capacity of the channel and with
smaller
amounts that are to be sent (which is both intuitively obvious).
(Multi)path success probability thus declines exponentially the more
uncertain channels are included.
I understand that the actual payment path finding is not part of the
spec
but I think my results should be relevant to the list since:
a) The payment pathfinding is currently based on trial and error
approach
which has consequences that have not been studied well in the context
of
the Lightning Network
b) All implementations will use some heuristics in order to achieve
pathfinding.
c) Quick path finding is a crucial for a good user experience.
d) The uncertainty of payment paths is frequently quoted as a major
criticism of the Lightning Network (c.f. [1]) and I believe the
methodology
of this paper can be used to address this.
The main breakthrough is that a very simple model that puts the
uncertainty of channel balances at its heart. We belief the
uncertainty of
channel balance values is the main reason why some payments take
several
attempts and thus take more time. With the help of probability theory
we
are able to define the channel success and failure probabilities and
similarly (multi)path success and failure probabilities. Other Failure
reasons could also be included to the probability distributions.
With the help of crawling small samples of the network we observe that
the
probability distributions of the channel balances can be estimated
well
with a uniform distribution (which was a little bit surprising) but
leads
to surprisingly easy formulas. We are able to quantify the
uncertainty in
the channels and use negative Bernoulli trials to compute the expected
number of attempts that are necessary to deliver a payment of a
particular
amount from one node to another participant of the network. This can
be
used to abort the trial and error path finding if the probability
becomes
to low (expected number of attempts too high)
We can mathematically show what people already knew (and draw
conclusions
like the mentioned ones from it):
a) smaller amounts have higher success probabilities
b) the success probability declines exponentially with the number of
uncertain channels in a (multi)path.
c) depending on the payment pair, amount and splitting strategy it can
be
decided into how many parts a payment should be split to achieve the
highest success probability.
d) In particular for small amounts splitting almost never makes sense.
We demonstrate that sorting paths by their descending success
probability
during the trial and error payment process (instead of currently used
heuristics like fees or route length) and updating the probabilities
from
current failures decreases the number of average attempts and produces
a
much faster delivery of payments.
Additionally we looked what happened if BOLT14 [2] was implemented or
nodes
otherwise would pro-actively rebalance their channels according to
previous
research [3] and realized that the observed prior distribution changes
from
uniform to normal. This is great as small payments become even more
likely
(as one would intuitively assume and as previously showed) Our results
show
that probabilisitic path finding on a rebalanced network works even
better
(as in fewer failed attempts) which is yet another hint why BOLT14
might be
a good idea. However as mentioned the results can be implemented even
without BOLT14 or without other protocol changes by any
implementation.
One consequence from the paper that is not discussed heavily within
the
paper that I find pretty interesting is that if implementations follow
the
recommendation to use a probabilistic approach they will tend to route
payments along high capacity channels. While the fee based routing can
easily be gamed by dumping fees it is much harder to provide more
liquidity. And if done this would actually provide a service to the
network. This means that nodes which provide a lot of liquidity and
thus
utility might be able to charge higher fees (as long as they are small
enough so that users are willing to pay them) which would probably
allow
the emergence of a real routing fee market.
One note on the question of MPP: In the last couple weeks I have been
collaborating with Christian Decker. I belief (by using the
methodology
from this paper) to also have a definite solution to the question of:
How to split a payment into k parts and how many funds to allocate to
each
path to increase the (multi)path success probability.
While this is is not addressed in the attached paper as we still need
to
run evaluations I can already share that an equal sized split as used
in
the paper (and by some implementations) is not preferable as one can
easily
see from this example:
Imagine one is to deliver 100 satoshi and has to paths with 1
uncertain
channel on each path. The first of capacity 101 and the second of 51.
Obviously trying to send 100 satoshi along the 101 capacity channel is
bad.
Similarly splitting 50/50 and sending 50 Satoshi along the 51 satoshi
capacity channel is also bad. Thus a split that allocates for example
67
Satoshi to the 101 capacity and 33 to the 51 satoshi channel seems way
more
reasonable. Actually 75/25 would probably be the best solution for
such a
setting. And no it is only random coincident that a binary splitter
would
have arrived at that split eventually (after potential miss trials)
There is way more math theory of how to actually solve the
optimization
problem in the general case and how to find a split and paths that
maximizes the probability of the attempts. I cannot share these
results yet
but I am pretty confident that there will be updates on that end very
soon.
with kind regards Rene
[0]: https://arxiv.org/abs/2103.08576 Security and Privacy of
Lightning
Network Payments with Uncertain Channel Balances
[1]:
https://www.whatbitcoindid.com/podcast/peter-rizuns-lightning-critique-fud-or-fair
[2]: https://github.com/lightningnetwork/lightning-rfc/pull/780
[3]:
https://lists.linuxfoundation.org/pipermail/lightning-dev/2019-December/002406.html
--
https://www.rene-pickhardt.de
Skype: rene.pickhardt
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