Theo Diamandis on Warpcast

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Simple blockspace pricing mechanisms are a good idea! In a new paper, @gaa, @ciamac, and I show that simple pricing rules are optimal against worst-case adversaries.

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In previous work (also with @pinged, @alexevans) we show that most pricing rules, including EIP-1559, are implicitly solving an optimization problem.

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This problem is to maximize the utility of included transactions, minus the loss incurred by the network, subject to transaction constraints (e.g., gas limits, conflicting txns, etc).

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While this problem is unsolvable in practice, we can construct an equivalent (dual) problem: find the fees which minimize the difference between the blockspace “supply” of the network and the blockspace “demand” of the users.

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Importantly, we can compute the gradient of this function. This means, we can update fees with a simple first-order algorithm like gradient descent, it’s regularized counterpart, or mirror descent.

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In fact, the EIP-1559 style update (as implemented in 4844) is an online mirror descent algorithm.

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But how good of an idea is this type of simple algorithm? We show that, on average, there is little difference in welfare between “correctly” setting fixed fees with oracular knowledge of all future transactions, and using these basic gradient descent-like algorithms (which only depend on observable quantities).

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This bound holds _even in the presence of adversaries_ who are only limited by a fixed (but perhaps very large) budget. Market clearing prices need not exist!

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Furthermore, we show a corresponding lower bound: in the presence of these adversaries, you cannot achieve better than O(1/sqrt(T)) regret.

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These results follow from standard analysis techniques in online convex optimization. We suspect there is a lot of interesting future work to be done here.

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Check out the paper for more https://angeris.github.io/papers/oco-fees.pdf

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