We consider minimizing a smooth function subject to a summation constraint over its variables. By exploiting a connection between the greedy 2-coordinate update for this problem and equality-constrained steepest descent in the 1-norm, we give a convergence rate for greedy selection under a proximal Polyak-Lojasiewicz assumption that is faster than random selection and independent of the problem dimension $n$. We then consider minimizing with both a summation constraint and bound constraints, as arises in the support vector machine dual problem. Existing greedy rules for this setting either guarantee trivial progress only or require $O(n^2)$ time to compute. We show that bound- and summation-constrained steepest descent in the L1-norm guarantees more progress per iteration than previous rules and can be computed in only $O(n \log n)$ time.

North star metrics and online experimentation play a central role in how technology companies improve their products. In many practical settings, however, evaluating experiments based on the north star metric directly can be difficult. The two most significant issues are 1) low sensitivity of the north star metric and 2) differences between the short-term and long-term impact on the north star metric. A common solution is to rely on proxy metrics rather than the north star in experiment evaluation and launch decisions. Existing literature on proxy metrics concentrates mainly on the estimation of the long-term impact from short-term experimental data. In this paper, instead, we focus on the trade-off between the estimation of the long-term impact and the sensitivity in the short term. In particular, we propose the Pareto optimal proxy metrics method, which simultaneously optimizes prediction accuracy and sensitivity. In addition, we give an efficient multi-objective optimization algorithm that outperforms standard methods. We applied our methodology to experiments from a large industrial recommendation system, and found proxy metrics that are eight times more sensitive than the north star and consistently moved in the same direction, increasing the velocity and the quality of the decisions to launch new features.

The development of applications based on artificial intelligence and implemented over wireless networks is increasingly rapidly and is expected to grow dramatically in the future. The resulting demand for the aggregation of large amounts of data has caused serious communication bottlenecks in wireless networks and particularly at the network edge. Over-the-air federated learning (OTA-FL), leveraging the superposition feature of multi-access channels (MACs), enables users at the network edge to share spectrum resources and achieves efficient and low-latency global model aggregation. This paper provides a holistic review of progress in OTA-FL and points to potential future research directions. Specifically, we classify OTA-FL from the perspective of system settings, including single-antenna OTA-FL, multi-antenna OTA-FL, and OTA-FL with the aid of the emerging reconfigurable intelligent surface (RIS) technology, and the contributions of existing works in these areas are summarized. Moreover, we discuss the trust, security and privacy aspects of OTA-FL, and highlight concerns arising from security and privacy. Finally, challenges and potential research directions are discussed to promote the future development of OTA-FL in terms of improving system performance, reliability, and trustworthiness. Specifical challenges to be addressed include model distortion under channel fading, the ineffective OTA aggregation of local models trained on substantially unbalanced data, and the limited accessibility and verifiability of individual local models.

Transfer learning transfers the knowledge acquired by a model from a source task to multiple downstream target tasks with minimal fine-tuning. The success of transfer learning at improving performance, especially with the use of large pre-trained models has made transfer learning an essential tool in the machine learning toolbox. However, the conditions under which the performance is transferable to downstream tasks are not understood very well. In this work, we analyze the transfer of performance for classification tasks, when only the last linear layer of the source model is fine-tuned on the target task. We propose a novel Task Transfer Analysis approach that transforms the source distribution (and classifier) by changing the class prior distribution, label, and feature spaces to produce a new source distribution (and classifier) and allows us to relate the loss of the downstream task (i.e., transferability) to that of the source task. Concretely, our bound explains transferability in terms of the Wasserstein distance between the transformed source and downstream task's distribution, conditional entropy between the label distributions of the two tasks, and weighted loss of the source classifier on the source task. Moreover, we propose an optimization problem for learning the transforms of the source task to minimize the upper bound on transferability. We perform a large-scale empirical study by using state-of-the-art pre-trained models and demonstrate the effectiveness of our bound and optimization at predicting transferability. The results of our experiments demonstrate how factors such as task relatedness, pretraining method, and model architecture affect transferability.

Binary optimization has a wide range of applications in combinatorial optimization problems such as MaxCut, MIMO detection, and MaxSAT. However, these problems are typically NP-hard due to the binary constraints. We develop a novel probabilistic model to sample the binary solution according to a parameterized policy distribution. Specifically, minimizing the KL divergence between the parameterized policy distribution and the Gibbs distributions of the function value leads to a stochastic optimization problem whose policy gradient can be derived explicitly similar to reinforcement learning. For coherent exploration in discrete spaces, parallel Markov Chain Monte Carlo (MCMC) methods are employed to sample from the policy distribution with diversity and approximate the gradient efficiently. We further develop a filter scheme to replace the original objective function by the one with the local search technique to broaden the horizon of the function landscape. Convergence to stationary points in expectation of the policy gradient method is established based on the concentration inequality for MCMC. Numerical results show that this framework is very promising to provide near-optimal solutions for quite a few binary optimization problems.

Online advertising has recently grown into a highly competitive and complex multi-billion-dollar industry, with advertisers bidding for ad slots at large scales and high frequencies. This has resulted in a growing need for efficient "auto-bidding" algorithms that determine the bids for incoming queries to maximize advertisers' targets subject to their specified constraints. This work explores efficient online algorithms for a single value-maximizing advertiser under an increasingly popular constraint: Return-on-Spend (RoS). We quantify efficiency in terms of regret relative to the optimal algorithm, which knows all queries a priori. We contribute a simple online algorithm that achieves near-optimal regret in expectation while always respecting the specified RoS constraint when the input sequence of queries are i.i.d. samples from some distribution. We also integrate our results with the previous work of Balseiro, Lu, and Mirrokni [BLM20] to achieve near-optimal regret while respecting both RoS and fixed budget constraints. Our algorithm follows the primal-dual framework and uses online mirror descent (OMD) for the dual updates. However, we need to use a non-canonical setup of OMD, and therefore the classic low-regret guarantee of OMD, which is for the adversarial setting in online learning, no longer holds. Nonetheless, in our case and more generally where low-regret dynamics are applied in algorithm design, the gradients encountered by OMD can be far from adversarial but influenced by our algorithmic choices. We exploit this key insight to show our OMD setup achieves low regret in the realm of our algorithm.

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms, including gradient-based methods, the exponential / multiplicative weights algorithm for learning in finite games, optimistic and bandit variants of the above, etc. In addition to providing an integrated view of these algorithms, our framework further allows us to obtain several new convergence results, both asymptotic and in finite time, in both continuous and finite games. Specifically, we provide a range of criteria for identifying classes of Nash equilibria and sets of action profiles that are attracting with high probability, and we also introduce the notion of coherence, a game-theoretic property that includes strict and sharp equilibria, and which leads to convergence in finite time. Importantly, our analysis applies to both oracle-based and bandit, payoff-based methods - that is, when players only observe their realized payoffs.

Bike sharing systems have been widely deployed around the world in recent years. A core problem in such systems is to reposition the bikes so that the distribution of bike supply is reshaped to better match the dynamic bike demand. When the bike-sharing company or platform is able to predict the revenue of each reposition task based on historic data, an additional constraint is to cap the payment for each task below its predicted revenue. In this paper, we propose an incentive mechanism called {\em TruPreTar} to incentivize users to park bicycles at locations desired by the platform toward rebalancing supply and demand. TruPreTar possesses four important economic and computational properties such as truthfulness and budget feasibility. Furthermore, we prove that even when the payment budget is tight, the total revenue still exceeds or equals the budget. Otherwise, TruPreTar achieves 2-approximation as compared to the optimal (revenue-maximizing) solution, which is close to the lower bound of at least $\sqrt{2}$ that we also prove. Using an industrial dataset obtained from a large bike-sharing company, our experiments show that TruPreTar is effective in rebalancing bike supply and demand and, as a result, generates high revenue that outperforms several benchmark mechanisms.

A large number of real-world optimization problems can be formulated as Mixed Integer Linear Programs (MILP). MILP solvers expose numerous configuration parameters to control their internal algorithms. Solutions, and their associated costs or runtimes, are significantly affected by the choice of the configuration parameters, even when problem instances have the same number of decision variables and constraints. On one hand, using the default solver configuration leads to suboptimal solutions. On the other hand, searching and evaluating a large number of configurations for every problem instance is time-consuming and, in some cases, infeasible. In this study, we aim to predict configuration parameters for unseen problem instances that yield lower-cost solutions without the time overhead of searching-and-evaluating configurations at the solving time. Toward that goal, we first investigate the cost correlation of MILP problem instances that come from the same distribution when solved using different configurations. We show that instances that have similar costs using one solver configuration also have similar costs using another solver configuration in the same runtime environment. After that, we present a methodology based on Deep Metric Learning to learn MILP similarities that correlate with their final solutions' costs. At inference time, given a new problem instance, it is first projected into the learned metric space using the trained model, and configuration parameters are instantly predicted using previously-explored configurations from the nearest neighbor instance in the learned embedding space. Empirical results on real-world problem benchmarks show that our method predicts configuration parameters that improve solutions' costs by up to 38% compared to existing approaches.

Impactful applications such as materials discovery, hardware design, neural architecture search, or portfolio optimization require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. While Bayesian optimization has recently made significant progress in solving such problems, an in-depth analysis reveals that the current state-of-the-art methods are not reliable. Their performances degrade substantially when the unknown optima of the function do not have a certain structure. To fill the need for a reliable algorithm for combinatorial and mixed spaces, this paper proposes Bounce that relies on a novel map of various variable types into nested embeddings of increasing dimensionality. Comprehensive experiments show that Bounce reliably achieves and often even improves upon state-of-the-art performance on a variety of high-dimensional problems.