  Dynamic AMM pools, as found in Temporal Function Market Making, rebalance
their holdings to a new desired ratio (e.g. moving from being 50-50 between two
assets to being 90-10 in favour of one of them) by introducing an arbitrage
opportunity that disappears when their holdings are in line with their target.
Structuring this arbitrage opportunity reduces to the problem of choosing the
sequence of portfolio weights the pool exposes to the market via its trading
function. Linear interpolation from start weights to end weights has been used
to reduce the cost paid by pools to arbitrageurs to rebalance. Here we obtain
the $\textit{optimal}$ interpolation in the limit of small weight changes
(which has the downside of requiring a call to a transcendental function) and
then obtain a cheap-to-compute approximation to that optimal approach that
gives almost the same performance improvement. We then demonstrate this method
on a range of market backtests, including simulating pool performance when
trading fees are present, finding that the new approximately-optimal method of
changing weights gives robust increases in pool performance. For a BTC-ETH-DAI
pool from July 2022 to June 2023, the increases of pool P\&L from
approximately-optimal weight changes is $\sim25\%$ for a range of different
strategies and trading fees.
