Autonomous robotic systems are of particular interest for many fields, especially those that can be dangerous for human intervention like search and rescue, and maintenance on rigs. However, motion planning in unstructured environment is still a hard problem for legged robots and their success depends largely on their ability to plan their paths robustly. Moreover, the method in which a controller deals with obstacles has great consequences on the planned trajectory, and these optimizations are quintessential in generating agile motions for real-world robots. Trajectory optimization is a common practice for generating motion for legged systems [1, 2, 3], since it can produce optimal trajectories which satisfy the physical and environmental constraints of the robot. However, the solution from trajectory optimization is only valid for a particular pair of initial and target positions, and one needs to re-plan if the pair changes.

Marketing is an important mechanism to increase user engagement and improve platform revenue, and heterogeneous causal learning can help develop more effective strategies. Most decision-making problems in marketing can be formulated as resource allocation problems and have been studied for decades. Existing works usually divide the solution procedure into two fully decoupled stages, i.e., machine learning (ML) and operation research (OR) -- the first stage predicts the model parameters and they are fed to the optimization in the second stage. However, the error of the predicted parameters in ML cannot be respected and a series of complex mathematical operations in OR lead to the increased accumulative errors. Essentially, the improved precision on the prediction parameters may not have a positive correlation on the final solution due to the side-effect from the decoupled design. In this paper, we propose a novel approach for solving resource allocation problems to mitigate the side-effects. Our key intuition is that we introduce the decision factor to establish a bridge between ML and OR such that the solution can be directly obtained in OR by only performing the sorting or comparison operations on the decision factor. Furthermore, we design a customized loss function that can conduct direct heterogeneous causal learning on the decision factor, an unbiased estimation of which can be guaranteed when the loss converges. As a case study, we apply our approach to two crucial problems in marketing: the binary treatment assignment problem and the budget allocation problem with multiple treatments. Both large-scale simulations and online A/B Tests demonstrate that our approach achieves significant improvement compared with state-of-the-art.

Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which they want to be matched. Viewing such an application as a multi-round matching problem on a bipartite compatibility graph between agents and resources, we show that a solution (i.e., a set of matchings, with one matching per round) can be found efficiently if one exists. To cope with situations where a solution does not exist, we consider two extensions. In the first extension, a benefit function is defined for each agent and the objective is to find a multi-round matching to maximize the total benefit. For a general class of benefit functions satisfying certain properties (including diminishing returns), we show that this multi-round matching problem is efficiently solvable. This class includes utilitarian and Rawlsian welfare functions. For another benefit function, we show that the maximization problem is NP-hard. In the second extension, the objective is to generate advice to each agent (i.e., a subset of requirements to be relaxed) subject to a budget constraint so that the agent can be matched. We show that this budget-constrained advice generation problem is NP-hard. For this problem, we develop an integer linear programming formulation as well as a heuristic based on local search. We experimentally evaluate our algorithms on synthetic networks and apply them to two real-world situations: shared office spaces and matching courses to classrooms.

As one of the most striking advances in online advertising, real-time bidding (RTB) [3] has received increasing attention since it improves the efficiency and transparency of the ad ecosystem [4]. In RTB, the publishing media sells ad impressions through public auctions, and advertisers bid on their targeting ad impressions in real-time and pay for their winning impressions. Therefore, it requires the bidding agent to make accurate user feedback predictions for each ad impression and determine a reasonable bidding price to maximize the long-term revenue [5] of the ad campaign. Figure 1 illustrates the entire process of an advertiser participating in bidding for an ad impression. Initially, the advertiser registers an ad campaign on the Demand Side Platform (DSP) and specifies the campaign's budget as well as targeting rules for each ad delivery period (usually a day). Bidding agents running on DSP participate in RTB on behalf of advertisers.

The fair-ranking problem, which asks to rank a given set of items to maximize utility subject to group fairness constraints, has received attention in the fairness, information retrieval, and machine learning literature. Recent works, however, observe that errors in socially-salient (including protected) attributes of items can significantly undermine fairness guarantees of existing fair-ranking algorithms and raise the problem of mitigating the effect of such errors. We study the fair-ranking problem under a model where socially-salient attributes of items are randomly and independently perturbed. We present a fair-ranking framework that incorporates group fairness requirements along with probabilistic information about perturbations in socially-salient attributes. We provide provable guarantees on the fairness and utility attainable by our framework and show that it is information-theoretically impossible to significantly beat these guarantees. Our framework works for multiple non-disjoint attributes and a general class of fairness constraints that includes proportional and equal representation. Empirically, we observe that, compared to baselines, our algorithm outputs rankings with higher fairness, and has a similar or better fairness-utility trade-off compared to baselines.

This paper aims to provide an unsupervised modelling approach that allows for a more flexible representation of text embeddings. It jointly encodes the words and the paragraphs as individual matrices of arbitrary column dimension with unit Frobenius norm. The representation is also linguistically motivated with the introduction of a novel similarity metric. The proposed modelling and the novel similarity metric exploits the matrix structure of embeddings. We then go on to show that the same matrices can be reshaped into vectors of unit norm and transform our problem into an optimization problem over the spherical manifold. We exploit manifold optimization to efficiently train the matrix embeddings. We also quantitatively verify the quality of our text embeddings by showing that they demonstrate improved results in document classification, document clustering, and semantic textual similarity benchmark tests.

Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many studies on structure learning with various types of data, the structure learning on the dynamic graph has not been explored yet, and thus we study the learning problem of node feature generation mechanism on such ubiquitous dynamic graph data. In a dynamic graph, we propose to simultaneously estimate contemporaneous relationships and time-lagged interaction relationships between the node features. These two kinds of relationships form a DAG, which could effectively characterize the feature generation process in a concise way. To learn such a DAG, we cast the learning problem as a continuous score-based optimization problem, which consists of a differentiable score function to measure the validity of the learned DAGs and a smooth acyclicity constraint to ensure the acyclicity of the learned DAGs. These two components are translated into an unconstraint augmented Lagrangian objective which could be minimized by mature continuous optimization techniques. The resulting algorithm, named GraphNOTEARS, outperforms baselines on simulated data across a wide range of settings that may encounter in real-world applications. We also apply the proposed approach on two dynamic graphs constructed from the real-world Yelp dataset, demonstrating our method could learn the connections between node features, which conforms with the domain knowledge.

Controllable image synthesis with user scribbles has gained huge public interest with the recent advent of text-conditioned latent diffusion models. The user scribbles control the color composition while the text prompt provides control over the overall image semantics. However, we note that prior works in this direction suffer from an intrinsic domain shift problem, wherein the generated outputs often lack details and resemble simplistic representations of the target domain. In this paper, we propose a novel guided image synthesis framework, which addresses this problem by modeling the output image as the solution of a constrained optimization problem. We show that while computing an exact solution to the optimization is infeasible, an approximation of the same can be achieved while just requiring a single pass of the reverse diffusion process. Additionally, we show that by simply defining a cross-attention based correspondence between the input text tokens and the user stroke-painting, the user is also able to control the semantics of different painted regions without requiring any conditional training or finetuning. Human user study results show that the proposed approach outperforms the previous state-of-the-art by over 85.32% on the overall user satisfaction scores. Project page for our paper is available at https://1jsingh.github.io/gradop.

Federated learning (FL) has emerged as a solution to deal with the risk of privacy leaks in machine learning training. This approach allows a variety of mobile devices to collaboratively train a machine learning model without sharing the raw on-device training data with the cloud. However, efficient edge deployment of FL is challenging because of the system/data heterogeneity and runtime variance. This paper optimizes the energy-efficiency of FL use cases while guaranteeing model convergence, by accounting for the aforementioned challenges. We propose FedGPO based on a reinforcement learning, which learns how to identify optimal global parameters (B, E, K) for each FL aggregation round adapting to the system/data heterogeneity and stochastic runtime variance. In our experiments, FedGPO improves the model convergence time by 2.4 times, and achieves 3.6 times higher energy efficiency over the baseline settings, respectively.

We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black box. To tackle this problem, we apply zeroth-order optimization techniques that combine smoothed gradient estimators with equilibrium-finding dynamics. We model players' strategies using artificial neural networks. In particular, we use randomized policy networks to model mixed strategies. These take noise in addition to an observation as input and can flexibly represent arbitrary observation-dependent, continuous-action distributions. Being able to model such mixed strategies is crucial for tackling continuous-action games that lack pure-strategy equilibria. We evaluate the performance of our method using an approximation of the Nash convergence metric from game theory, which measures how much players can benefit from unilaterally changing their strategy. We apply our method to continuous Colonel Blotto games, single-item and multi-item auctions, and a visibility game. The experiments show that our method can quickly find high-quality approximate equilibria. Furthermore, they show that the dimensionality of the input noise is crucial for performance. To our knowledge, this paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information.