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Learning from Streaming Data when Users Choose
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Formalizes streaming users who choose among competing services with bounded rationality and proposes MSGD, a decentralized single-user gradient update, proving almost-sure convergence to stationary points of the overall user loss.
Problem
Competing services that update models incrementally from streaming user data face feedback loops, since user choices determine which data each service sees and each service observes only the users that choose it; the goal is to minimize average user loss under imperfectly rational user choice.
Approach
Users pick the lowest-loss service with probability 1-zeta and a uniform random service otherwise; each chosen service takes a single gradient step on the one user's loss. The paper shows the expected single-user update is parallel to the gradient of the overall loss, which yields convergence to stationary points of that objective.
Key results
- On ACSEmployment with k=3, MSGD achieves higher overall welfare than Full Information when zeta is small (high rationality), while Full Information wins when zeta is large.
- MSGD achieves higher accuracy on induced subpopulations than Full Information, and this accuracy grows with k, but whole-population accuracy is lower than Full Information.
- Convergence of the overall objective and iterates is shown almost surely under stepsize and compactness assumptions, with eta_t = eta_c/t for iterate convergence.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MSGD instead of Full Information when users choose with high rationality | MSGD vs. Full Information · MovieLens10M and ACSEmployment | overall loss | Helped |
| Use MSGD instead of Full Information when users choose mostly at random | MSGD vs. Full Information · MovieLens10M and ACSEmployment | overall loss | Hurt |
| Increase user-random-choice probability ζ (ablation) | MSGD · MovieLens10M and ACSEmployment | overall loss | Hurt |
| Use MSGD instead of Full Information | ACSEmployment · ACSEmployment induced subpopulations | accuracy | Helped |
| Use MSGD instead of Full Information | ACSEmployment · ACSEmployment whole population | accuracy | Hurt |
| Increase the number of services k (ablation) | MSGD · ACSEmployment induced subpopulations | accuracy | Helped |
| Increase the number of services k (ablation) | MSGD · ACSEmployment whole population | accuracy | Hurt |
| Increase the number of services k (ablation) | Full Information · ACSEmployment | accuracy | No clear effect |
Surprising findings
- MSGD on the whole population can perform worse than Full Information, and whole-population accuracy can decrease with more training steps.
- Full Information converges more slowly than MSGD when users choose with high rationality.
Limitations
- Convergence guarantees only to stationary points of a non-convex objective, not global optima.
- Boltzmann-rational user choice is not covered theoretically; only shown empirically in appendix.
- Whole-population accuracy can be worse than full information due to specialization.
Experimental setup
Datasets: MovieLens10M ACSEmployment (folktables)
Benchmarks: MovieLens10M ACSEmployment (folktables)
Metrics: overall loss f(Theta) accuracy on induced subpopulation accuracy on whole population accumulated parameter update distance
Baselines: Full Information gradient descent
Builds on: performative prediction multi-player performative prediction stochastic gradient descent
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