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We design online algorithms for the fair allocation of public goods to a setof $N$ agents over a sequence of $T$ rounds and focus on improving theirperformance using predictions. In the basic model, a public good arrives ineach round, the algorithm learns every agent's value for the good, and mustirrevocably decide the amount of investment in the good without exceeding atotal budget of $B$ across all rounds. The algorithm can utilize (potentiallyinaccurate) predictions of each agent's total value for all the goods toarrive. We measure the performance of the algorithm using a proportionalfairness objective, which informally demands that every group of agents berewarded in proportion to its size and the cohesiveness of its preferences.  In the special case of binary agent preferences and a unit budget, we showthat $O(\log N)$ proportional fairness can be achieved without using anypredictions, and that this is optimal even if perfectly accurate predictionswere available. However, for general preferences and budget no algorithm canachieve better than $\Theta(T/B)$ proportional fairness without predictions. Weshow that algorithms with (reasonably accurate) predictions can do much better,achieving $\Theta(\log (T/B))$ proportional fairness. We also extend thisresult to a general model in which a batch of $L$ public goods arrive in eachround and achieve $O(\log (\min(N,L) \cdot T/B))$ proportional fairness. Ourexact bounds are parametrized as a function of the error in the predictions andthe performance degrades gracefully with increasing errors.

Proportionally Fair Online Allocation of Public Goods with Predictions