Devon R. Graham

Devon R. Graham, Kevin Leyton-Brown, Tim Roughgarden

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

Devon R. Graham, Kevin Leyton-Brown, Tim Roughgarden

We present the first nontrivial procedure for configuring heuristic algorithms to maximize the utility provided to their end users while also offering theoretical guarantees about performance. Existing procedures seek configurations that minimize expected runtime. However, very recent theoretical work argues that expected runtime minimization fails to capture algorithm designers' preferences. Here we show that the utilitarian objective also confers significant algorithmic benefits. Intuitively, this is because mean runtime is dominated by extremely long runs even when they are incredibly rare; indeed, even when an algorithm never gives rise to such long runs, configuration procedures that provably minimize mean runtime must perform a huge number of experiments to demonstrate this fact. In contrast, utility is bounded and monotonically decreasing in runtime, allowing for meaningful empirical bounds on a configuration's performance. This paper builds on this idea to describe effective and theoretically sound configuration procedures. We prove upper bounds on the runtime of these procedures that are similar to theoretical lower bounds, while also demonstrating their performance empirically.

Devon Graham, Satish Kumar Sarraf, Taylor Lundy et al.

On-street parking is convenient, but has many disadvantages: on-street spots come at the expense of other road uses such as traffic lanes, transit lanes, bike lanes, or parklets; drivers looking for parking contribute substantially to traffic congestion and hence to greenhouse gas emissions; safety is reduced both due to the fact that drivers looking for spots are more distracted than other road users and that people exiting parked cars pose a risk to cyclists. These social costs may not be worth paying when off-street parking lots are nearby and have surplus capacity. To see where this might be true in downtown Vancouver, we used artificial intelligence techniques to estimate the amount of time it would take drivers to both park on and off street for destinations throughout the city. For on-street parking, we developed (1) a deep-learning model of block-by-block parking availability based on data from parking meters and audits and (2) a computational simulation of drivers searching for an on-street spot. For off-street parking, we developed a computational simulation of the time it would take drivers drive from their original destination to the nearest city-owned off-street lot and then to queue for a spot based on traffic and lot occupancy data. Finally, in both cases we also computed the time it would take the driver to walk from their parking spot to their original destination. We compared these time estimates for destinations in each block of Vancouver's downtown core and each hour of the day. We found many areas where off street would actually save drivers time over searching the streets for a spot, and many more where the time cost for parking off street was small. The identification of such areas provides an opportunity for the city to repurpose valuable curbside space for community-friendly uses more in line with its transportation goals.

Devon Graham, Junhao Wang, Siamak Ravanbakhsh

The relational model is a ubiquitous representation of big-data, in part due to its extensive use in databases. In this paper, we propose the Equivariant Entity-Relationship Network (EERN), which is a Multilayer Perceptron equivariant to the symmetry transformations of the Entity-Relationship model. To this end, we identify the most expressive family of linear maps that are exactly equivariant to entity relationship symmetries, and further show that they subsume recently introduced equivariant maps for sets, exchangeable tensors, and graphs. The proposed feed-forward layer has linear complexity in the data and can be used for both inductive and transductive reasoning about relational databases, including database embedding, and the prediction of missing records. This provides a principled theoretical foundation for the application of deep learning to one of the most abundant forms of data. Empirically, EERN outperforms different variants of coupled matrix tensor factorization in both synthetic and real-data experiments.

Robert Kleinberg, Kevin Leyton-Brown, Brendan Lucier et al.

Algorithm configuration methods optimize the performance of a parameterized heuristic algorithm on a given distribution of problem instances. Recent work introduced an algorithm configuration procedure ("Structured Procrastination") that provably achieves near optimal performance with high probability and with nearly minimal runtime in the worst case. It also offers an $\textit{anytime}$ property: it keeps tightening its optimality guarantees the longer it is run. Unfortunately, Structured Procrastination is not $\textit{adaptive}$ to characteristics of the parameterized algorithm: it treats every input like the worst case. Follow-up work ("LeapsAndBounds") achieves adaptivity but trades away the anytime property. This paper introduces a new algorithm, "Structured Procrastination with Confidence", that preserves the near-optimality and anytime properties of Structured Procrastination while adding adaptivity. In particular, the new algorithm will perform dramatically faster in settings where many algorithm configurations perform poorly. We show empirically both that such settings arise frequently in practice and that the anytime property is useful for finding good configurations quickly.

Jason Hartford, Devon R Graham, Kevin Leyton-Brown et al.

We use deep learning to model interactions across two or more sets of objects, such as user-movie ratings, protein-drug bindings, or ternary user-item-tag interactions. The canonical representation of such interactions is a matrix (or a higher-dimensional tensor) with an exchangeability property: the encoding's meaning is not changed by permuting rows or columns. We argue that models should hence be Permutation Equivariant (PE): constrained to make the same predictions across such permutations. We present a parameter-sharing scheme and prove that it could not be made any more expressive without violating PE. This scheme yields three benefits. First, we demonstrate state-of-the-art performance on multiple matrix completion benchmarks. Second, our models require a number of parameters independent of the numbers of objects, and thus scale well to large datasets. Third, models can be queried about new objects that were not available at training time, but for which interactions have since been observed. In experiments, our models achieved surprisingly good generalization performance on this matrix extrapolation task, both within domains (e.g., new users and new movies drawn from the same distribution used for training) and even across domains (e.g., predicting music ratings after training on movies).