Source-linked AI summary
Rewarding High-Quality Data via Influence Functions
Adam Richardson, Aris Filos-Ratsikas, Boi Faltings
TL;DR
Federated-learning research has focused on privacy, while rewarding self-interested providers according to data quality remains an open challenge. The paper bases payments on data-point influence for linear regression and reports truthful reporting as a game-theoretic equilibrium.
Problem
Federated-learning research has focused on privacy rather than rewarding providers according to data quality, even though collecting accurate data can require costly effort.
Source: §1 · p. 1Method
For linear regression, the scheme bases payments on data-point influence, approximates influence for sequential batch processing, and corrects for its difference from overall loss change.
Source: Influence and Incentive Schemes · p. 3, §3.1 · p. 3, §5 · p. 6Results
The authors report truthful reporting as a game-theoretic equilibrium and say real-dataset evaluations confirm their theoretical findings.
Source: Influence and Incentive Schemes · p. 3, §5 · p. 6Takeaways & Limitations
The framework targets quality- and timing-sensitive compensation, and allows a Center's nonlinear utility with loss to be passed on to payments.
Source: §5 · p. 6The analysis assumes linear regression, although the authors say the approach extends to other regression models.
Source: §2 · p. 2
Abstract
from arXiv · showhide
We consider a crowdsourcing data acquisition scenario, such as federated learning, where a Center collects data points from a set of rational Agents, with the aim of training a model. For linear regression models, we show how a payment structure can be designed to incentivize the agents to provide high-quality data as early as possible, based on a characterization of the influence that data points have on the loss function of the model. Our contributions can be summarized as follows: (a) we prove theoretically that this scheme ensures truthful data reporting as a game-theoretic equilibrium and further demonstrate its robustness against mixtures of truthful and heuristic data reports, (b) we design a procedure according to which the influence computation can be efficiently approximated and processed sequentially in batches over time, (c) we develop a theory that allows correcting the difference between the influence and the overall change in loss and (d) we evaluate our approach on real datasets, confirming our theoretical findings.
1 Introduction
The paper addresses how to reward costly, self-interested data providers for useful and timely contributions. It proposes influence-based payments and studies their incentive properties, sequential implementation, and relation to prior work.
1 Introduction
- Federated learning research had focused on privacy rather than rewarding agents according to how useful their contributed data is for learning.Because accurate data collection can be costly, the paper motivates compensation that encourages agents to exert effort.Source: §1 · p. 1
1.1 Our Approach
- The proposed scheme rewards agents according to how their data changes model loss, using influence to measure each point’s effect on accuracy.The Center pays for useful data, with a guarantee that total acquisition cost is bounded.Source: §1.1 · p. 1
- Truthful sampling and reporting is an equilibrium under reasonable assumptions, and the scheme remains truthful with independent testing data or a test set built from reports that include uninformed agents.The approach seeks to make effortful data collection preferable to heuristic reporting.Source: §1.1 · pp. 1–2
- Influence is approximated by up-weighting training points, extending Koh and Liang [2017] with an approximation reported to be close to exact influence and faster on sufficiently high-dimensional datasets.The paper also evaluates its theoretical findings on real and generated data.Source: §1.1 · p. 2
- For sequential data collection, agents are rewarded in batches, with earlier contributions receiving more; the paper considers M-Inclusive and M-Exclusive influence calculations.It initializes the model with uniform samples to represent a knowledge-less Center and analyzes how initial points affect the relation between influence and loss decrease.Source: §1.1 · p. 2
1.2 Related Work
- Related work addresses strategic influence on learned models, privacy compensation, peer-based elicitation, and data valuation, while Cai et al. [2015] assumes known effort–accuracy functions and an effort-only strategy space.The paper instead requires only a known bound on effort cost and allows providers to choose which data to supply.Source: §1.2 · p. 2
2 Setting and Foundations
The setting is a Center learning a regression model from agents who incur effort to provide data. The scheme uses each report’s influence on test loss to set payments, and the paper argues truthful reporting is an equilibrium under stated assumptions.
2 Setting and Foundations
- The formal setting assumes a linear regression model with non-negative sample loss, while noting that the general approach extends to other regression models.Agents supply points to a Center that wants to learn the model.Source: §2 · p. 2
Influence and Incentive Schemes
- An incentive scheme maps data points to payments and is designed to cover effort costs while rewarding points that improve model accuracy.Influence is defined through the difference in test-set risk with and without a point.Source: Influence and Incentive Schemes · p. 3
- The truthful strategy is a Bayes–Nash equilibrium when agents believe observation errors have mean zero and all other agents report truthfully.The proof argues truthful reports move the learned model toward the true optimum in expectation.Source: Influence and Incentive Schemes · p. 3
- The equilibrium argument also requires payments to increase with influence and to cover the cost of effort when reports are truthful.This connects the reward for useful data to participation incentives.Source: Influence and Incentive Schemes · p. 3
3 Methods
The methods approximate each data point’s influence, process reports in batches, and calibrate summed influences against the overall change in risk. They also analyze how initialization and reporting heuristics affect incentives.
3.1 Influence Approximation
- For a fixed test set, the approximation can reduce computation time at sufficiently high input dimensions, although its runtime grows faster with the number of test points.Figure 1 compares exact and approximate influence computation over 2,000 training points.Source: §3.1 · p. 3, Figure 1 · p. 4
3.2 Batch Processing
- Batch processing computes the inverse Hessian once per batch, and the analysis says it incentivizes earlier reports because exact influence is O(1/n^2) in expectation.The authors report that Figure 2 empirically shows this early-reporting effect; influence decreases rapidly after the first few batches.Source: §3.2 · p. 4, Figure 2 · p. 4
3.3 Initializing the Model
- The initial model represents the Center’s prior knowledge; with no prior knowledge, the paper uses samples from a uniform distribution within appropriate bounds.The paper also describes prior data or samples from a known model distribution as alternatives for initialization.Source: §3.3 · p. 4
3.4 M-Inclusive and M-Exclusive
- M-Inclusive evaluates points with the current batch included, while M-Exclusive evaluates them as additions to prior data; normalization can make expected summed influence equal the overall risk change.The two methods are equivalent at batch size one, when summed influence equals the overall risk change.Source: §3.4 · pp. 4–5
3.5 Heuristic Reporting
- With an independent test set, truthful reports are incentivized and heuristic reporters receive negative rewards; with a mixed test set, truthful reporters need a majority only when the correct model’s inherent error is higher.When the correct model’s inherent error is lower than the heuristic model’s, truthful-report incentives can persist without a majority of truthful reporters.Source: §3.5 · pp. 5–6
4 Experimental Results
Experiments on multiple datasets show that the Second Order Approximation produces better influence estimates than the First Order Approximation from Koh and Liang [2017]. Simulations also compare the M-Inclusive and M-Exclusive batch ratios with theoretical results.
4 Experimental Results
- The simulations covered linear-generated data and UCI datasets including wine, air quality, crime, and Parkinsons.The wine datasets predict a quality metric; the air-quality and crime datasets use C6H6(GT) and ViolentCrimesPerPop as their predicted attributes, respectively.Source: §4 · p. 6
- Across all datasets, the Second Order Approximation produces much lower absolute and relative absolute errors than Koh and Liang [2017]’s First Order Approximation.The comparison is reported in Table 1.Source: §4 · p. 6
- For the M-Inclusive and M-Exclusive evaluation, simulations used 1,500 training points and 10 trials per dataset at each batch size; the paper shows the 500-initial-point case.The authors report that simulations with 20, 100, and 200 initial points showed the same relationship.Source: §4 · p. 6
5 Conclusion
The paper presents an influence-based incentive scheme for regression data collection, with truthful reporting as a game-theoretic equilibrium and incentives for early, high-quality data. It develops batch processing and influence corrections, evaluates the theory on multiple datasets, and notes that privacy remains unaddressed.
5 Conclusion
- For regression models, the proposed influence-based payments make truthful reporting of accurate data a game-theoretic equilibrium and reward high-quality data contributed early.The scheme is also analyzed for agents who report heuristically without collecting actual data.Source: §5 · p. 6
- The paper develops batch processing for sequential data collection and a theory to correct the difference between influence and overall change in loss.The payment scheme can also incorporate a Center’s utility function when it is nonlinear in model loss.Source: §5 · p. 6
- The authors empirically validate their theoretical results on multiple datasets.Source: §5 · p. 6
- Privacy is not addressed, though the authors identify multiparty computation as a possible way to carry out the payment calculations privately and leave it for future work.Source: §5 · p. 6