In Auto campaigns, Amazon quietly retunes your bid for every search. In Manual campaigns, you commit to a single number, and that number is reused for every search the keyword matches. This is a plain-language tour of a recent Amazon research paper that works out the mathematically best way to choose those numbers. Play with each widget; the ideas are the slider, not the formula.
Every time a shopper types a query, Amazon runs a lightning-fast auction to decide which ads show. Your bid decides two things at once: how often you win, and how much you pay.
Campaigns come in two flavours:
Manual Targeting still drives ~30% of advertisers, people who want direct control, or who lack the data for automation to shine. And here’s the rub: a keyword like “running shoes” matches a laser-relevant long-tail search, a vague head term, and outright junk, all forced to share one bid. Picking that one number well is the entire game. OPTIMUS is the recipe for picking it.
Before choosing a bid, you need to know what a single search opportunity can earn. It’s a short chain that every advertiser half-knows:
Win the auction → ad is shown → shopper clicks (CTR) → shopper buys (CVR) → you collect the price. You only pay when someone clicks, and because it’s a second-price auction, you pay just enough to beat the next competitor, not your full bid.
Drag the bid below. Watch a higher bid win more auctions (good) but the curve flatten and your ACOS creep up (the cost of greed).
Here’s the heart of the Manual-Targeting problem. A single keyword matches very different searches. The paper calls them heterogeneous: different click rates, different conversion rates, different competition. Yet they’re stuck with the same bid.
Below, one bid is applied to three real-flavoured searches that the keyword “running shoes” might match. Slide it and watch the verdict flip from 🟢 profitable to 🔴 loss at the same moment, for different searches.
Zoom out from one search to a whole keyword. As you raise its bid, both your sales and your spend climb, but not in step. The first dollars are cheap and effective; later dollars chase auctions you barely wanted. The sales-vs-spend curve bends over.
The single most important quantity in the whole paper lives on this curve: the slope: “what does my next dollar of spend buy me in sales?” The researchers call it the marginal return. Drag the point and watch the next-dollar value shrink as you spend more.
Now the punchline. You have a fixed budget and several keywords, each with its own diminishing-returns curve. Where should the money go?
Spread your budget so that the next dollar on every keyword would buy the same amount of sales. If keyword A’s next dollar would earn $3 of sales while keyword B’s would earn only $2, you’re leaving money on the table: move a dollar from B to A. Keep moving until they’re level. That balance point is provably the best you can do.
The paper proves this is the unique optimum (they equalise the “marginal return” across every targeting clause). Below you control the budget. Compare splitting it evenly versus letting OPTIMUS balance the last dollar. Watch total sales, and watch the three “next-dollar” bars on the right line up level under OPTIMUS.
Balancing every keyword by hand would be hopeless: real campaigns have 50–200 of them. The clever trick is to replace that whole juggling act with a single dial, which the paper calls λ (“lambda”). Think of λ as your minimum acceptable return on the last dollar:
Turn the dial up (demand a high return) and every keyword pulls back: total spend falls. Turn it down and they all lean in: spend rises. So there’s exactly one setting of λ where the total spend equals your budget. The computer finds it by simple trial-and-halving (a binary search): too much spend? raise λ; too little? lower it. A handful of steps and it’s done.
That’s the entire OPTIMUS algorithm. To feed it, the paper plugs in three forecasts trained on Amazon’s historical auction logs: how often each bid wins (the bid landscape), the CTR, and the CVR. Because it’s “model-agnostic,” better forecasts simply make the bids better. It runs in under 10 seconds per campaign and scales to millions of them.
The team tested OPTIMUS two ways: by replaying ~4 billion real auction logs (“what if we’d bid differently?”), and with live A/B tests against expert human-set bids on a major e-commerce platform.
The gains came precisely from the rule in Widget 5: OPTIMUS pulls money out of low-efficiency keywords and pours it into high-efficiency ones until the last dollar is balanced everywhere. A nice side effect: by favouring keywords with strong query–product relevance (which tend to convert well), it preferentially wins relevant auctions, so click and conversion rates rise too. Better for the advertiser and the shopper. Interestingly, the biggest wins were on newer campaigns, where there’s the least human intuition to lean on.
OPTIMUS assumes the market is reasonably stable (yesterday’s competition resembles tomorrow’s) and that its three forecasts are trustworthy point estimates. When competition swings wildly or data is thin, those assumptions wobble, which is exactly where the authors point their future work (robustness under uncertainty, non-stationary markets). The core idea, though, is timeless: balance the last dollar.
In Manual Targeting you can’t bid per search, so don’t try. Instead, fund your keywords until one more dollar would earn the same everywhere, and the math guarantees you’ve squeezed the most sales out of your budget.