[Lightning-dev] Towards more reliable payment path finding via probabilistic modeling the uncertainty of channel balance

Thu Mar 18 08:27:35 UTC 2021

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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