Algorithms and Theory

Google’s mission presents many exciting algorithmic and optimization challenges across different product areas including Search, Ads, Social, and Google Infrastructure. These include optimizing internal systems such as scheduling the machines that power the numerous computations done each day, as well as optimizations that affect core products and users, from online allocation of ads to page-views to automatic management of ad campaigns, and from clustering large-scale graphs to finding best paths in transportation networks. Other than employing new algorithmic ideas to impact millions of users, Google researchers contribute to the state-of-the-art research in these areas by publishing in top conferences and journals.

Recent Publications

Preview abstract The federated learning paradigm has motivated the development of methods for aggregating multiple client updates into a global server model, without sharing client data. Many federated learning algorithms, including the canonical Federated Averaging (FedAvg), take a direct (possibly weighted) average of the client parameter updates, motivated by results in distributed optimization. In this work, we adopt a function space perspective and propose a new algorithm, FedFish, that aggregates local approximations to the functions learned by clients, using an estimate based on their Fisher information. We evaluate FedFish on realistic, large-scale cross-device benchmarks. While the performance of FedAvg can suffer as client models drift further apart, we demonstrate that FedFish is more robust to longer local training. Our evaluation across several settings in image and language benchmarks shows that FedFish outperforms FedAvg as local training epochs increase. Further, FedFish results in global networks that are more amenable to efficient personalization via local fine-tuning on the same or shifted data distributions. For instance, federated pretraining on the C4 dataset, followed by few-shot personalization on Stack Overflow, results in a 7% improvement in next-token prediction by FedFish over FedAvg. View details
Delphic Offline Reinforcement Learning under Nonidentifiable Hidden Confounding
Alizée Pace
Hugo Yèche
Bernhard Schölkopf
Gunnar Rätsch
The Twelfth International Conference on Learning Representations(2024)
Preview abstract A prominent challenge of offline reinforcement learning (RL) is the issue of hidden confounding. There, unobserved variables may influence both the actions taken by the agent and the outcomes observed in the data. Hidden confounding can compromise the validity of any causal conclusion drawn from the data and presents a major obstacle to effective offline RL. In this paper, we tackle the problem of hidden confounding in the nonidentifiable setting. We propose a definition of uncertainty due to confounding bias, termed delphic uncertainty, which uses variation over compatible world models, and differentiate it from the well known epistemic and aleatoric uncertainties. We derive a practical method for estimating the three types of uncertainties, and construct a pessimistic offline RL algorithm to account for them. Our method does not assume identifiability of the unobserved confounders, and attempts to reduce the amount of confounding bias. We demonstrate through extensive experiments and ablations the efficacy of our approach on a sepsis management benchmark, as well as real electronic health records. Our results suggest that nonidentifiable confounding bias can be addressed in practice to improve offline RL solutions. View details
Preview abstract A lexicographic maximum of a set $X \subseteq R^n$ is a vector in $X$ whose smallest component is as large as possible, and subject to that requirement, whose second smallest component is as large as possible, and so on for the third smallest component, etc. Lexicographic maximization has numerous practical and theoretical applications, including fair resource allocation, analyzing the implicit regularization of learning algorithms, and characterizing refinements of game-theoretic equilibria. We prove that a minimizer in $X$ of the exponential loss function $L_c(x) = \sum_i \exp(-c x_i)$ converges to a lexicographic maximum of $X$ as $c \rightarrow \infty$, provided that $X$ is stable in the sense that a well-known iterative method for finding a lexicographic maximum of $X$ cannot be made to fail simply by reducing the required quality of each iterate by an arbitrarily tiny degree. Our result holds for both near and exact minimizers of the exponential loss, while earlier convergence results made much stronger assumptions about the set $X$ and only held for the exact minimizer. We are aware of no previous results showing a connection between the iterative method for computing a lexicographic maximum and exponential loss minimization. We show that every convex polytope is stable, but that there exist compact, convex sets that are not stable. We also provide the first analysis of the convergence rate of an exponential loss minimizer (near or exact) and discover a curious dichotomy: While the two smallest components of the vector converge to the lexicographically maximum values very quickly (at roughly the rate $(\log n)/c$), all other components can converge arbitrarily slowly. View details
Preview abstract Given a training data-set $\mathcal{S}$, and a reference data-set $\mathcal{T}$, we design a simple and efficient algorithm to reweigh the loss function such that the limiting distribution of the neural network weights that result from training on $\mathcal{S}$ approaches the limiting distribution that would have resulted by training on $\mathcal{T}$. Such reweighing can be used to correct for Train-Test distribution shift, when we don't have access to the labels of $\mathcal{T}$. It can also be used to perform (soft) multi-criteria optimization on neural nets, when we have access to the labels of $\mathcal{T}$, but $\mathcal{S}$ and $\mathcal{T}$ have few common points. As a motivating application, we train a graph neural net to recognize small molecule binders to MNK2 (a MAP Kinase, responsible for cell signaling) which are non-binders to MNK1 (a very similar protein), even in the absence of training data common to both data-sets. We are able to tune the reweighing parameters so that overall change in holdout loss is negligible, but the selectivity, i.e., the fraction of top 100 MNK2 binders that are MNK1 non-binders, increases from 54\% to 95\%, as a result of our reweighing. We expect the algorithm to be applicable in other settings as well, since we prove that when the metric entropy of the input data-sets is bounded, our random sampling based greedy algorithm outputs a close to optimal reweighing, i.e., the two invariant distributions of network weights will be provably close in total variation distance. View details
Preview abstract Effective model calibration is a critical and indispensable component in developing Media Mix Models (MMMs). One advantage of Bayesian-based MMMs lies in their capacity to accommodate the information from experiment results and the modelers' domain knowledge about the ad effectiveness by setting priors for the model parameters. However, it remains ambiguous about how and which Bayesian priors should be tuned for calibration purpose. In this paper, we propose a new calibration method through model reparameterization. The reparameterized model includes Return on Ads Spend (ROAS) as a model parameter, enabling straightforward adjustment of its prior distribution to align with either experiment results or the modeler's prior knowledge. The proposed method also helps address several key challenges regarding combining MMMs and incrementality experiments. We use simulations to demonstrate that our approach can significantly reduce the bias and uncertainty in the resultant posterior ROAS estimates. View details
First Passage Percolation with Queried Hints
Kritkorn Karntikoon
Aaron Schild
Yiheng Shen
Ali Sinop
Preview abstract Optimization problems are ubiquitous throughout the modern world. In many of these applications, the input is inherently noisy and it is expensive to probe all of the noise in the input before solving the relevant optimization problem. In this work, we study how much of that noise needs to be queried in order to obtain an approximately optimal solution to the relevant problem. We focus on the shortest path problem in graphs, where one may think of the noise as coming from real-time traffic. We consider the following model: start with a weighted base graph $G$ and multiply each edge weight by an independently chosen, uniformly random number in $[1,2]$ to obtain a random graph $G'$. This model is called \emph{first passage percolation}. Mathematicians have studied this model extensively when $G$ is a $d$-dimensional grid graph, but the behavior of shortest paths in this model is still poorly understood in general graphs. We make progress in this direction for a class of graphs that resembles real-world road networks. Specifically, we prove that if the geometric realization of $G$ has constant doubling dimension, then for a given $s-t$ pair, we only need to probe the weights on $((\log n) / \epsilon)^{O(1)}$ edges in $G'$ in order to obtain a $(1 + \epsilon)$-approximation to the $s-t$ distance in $G'$. We also demonstrate experimentally that this result is pessimistic -- one can even obtain a short path in $G'$ with a small number of probes to $G'$. View details