Swati Gupta

LG
h-index8
20papers
201citations
Novelty51%
AI Score55

20 Papers

CVJan 23
AnyView: Synthesizing Any Novel View in Dynamic Scenes

Basile Van Hoorick, Dian Chen, Shun Iwase et al. · gatech

Modern generative video models excel at producing convincing, high-quality outputs, but struggle to maintain multi-view and spatiotemporal consistency in highly dynamic real-world environments. In this work, we introduce \textbf{AnyView}, a diffusion-based video generation framework for \emph{dynamic view synthesis} with minimal inductive biases or geometric assumptions. We leverage multiple data sources with various levels of supervision, including monocular (2D), multi-view static (3D) and multi-view dynamic (4D) datasets, to train a generalist spatiotemporal implicit representation capable of producing zero-shot novel videos from arbitrary camera locations and trajectories. We evaluate AnyView on standard benchmarks, showing competitive results with the current state of the art, and propose \textbf{AnyViewBench}, a challenging new benchmark tailored towards \emph{extreme} dynamic view synthesis in diverse real-world scenarios. In this more dramatic setting, we find that most baselines drastically degrade in performance, as they require significant overlap between viewpoints, while AnyView maintains the ability to produce realistic, plausible, and spatiotemporally consistent videos when prompted from \emph{any} viewpoint. Results, data, code, and models can be viewed at: https://tri-ml.github.io/AnyView/

AIApr 10, 2023
Artificial Intelligence/Operations Research Workshop 2 Report Out

John Dickerson, Bistra Dilkina, Yu Ding et al.

This workshop Report Out focuses on the foundational elements of trustworthy AI and OR technology, and how to ensure all AI and OR systems implement these elements in their system designs. Four sessions on various topics within Trustworthy AI were held, these being Fairness, Explainable AI/Causality, Robustness/Privacy, and Human Alignment and Human-Computer Interaction. Following discussions of each of these topics, workshop participants also brainstormed challenge problems which require the collaboration of AI and OR researchers and will result in the integration of basic techniques from both fields to eventually benefit societal needs.

DCApr 11, 2023
TACOS: Topology-Aware Collective Algorithm Synthesizer for Distributed Machine Learning

William Won, Midhilesh Elavazhagan, Sudarshan Srinivasan et al.

The surge of artificial intelligence, particularly large language models, has driven the rapid development of large-scale machine learning clusters. Executing distributed models on these clusters is often constrained by communication overhead, making efficient utilization of available network resources crucial. As a result, the routing algorithm employed for collective communications (i.e., collective algorithms) plays a pivotal role in determining overall performance. Unfortunately, existing collective communication libraries for distributed machine learning are limited by a fixed set of basic collective algorithms. This limitation hinders communication optimization, especially in modern clusters with heterogeneous and asymmetric topologies. Furthermore, manually designing collective algorithms for all possible combinations of network topologies and collective patterns requires heavy engineering and validation efforts. To address these challenges, this paper presents TACOS, an autonomous synthesizer capable of automatically generating topology-aware collective algorithms tailored to specific collective patterns and network topologies. TACOS is highly flexible, synthesizing an All-Reduce algorithm for a heterogeneous 128-NPU system in just 1.08 seconds, while achieving up to a 4.27x performance improvement over state-of-the-art synthesizers. Additionally, TACOS demonstrates better scalability with polynomial synthesis times, in contrast to NP-hard approaches which only scale to systems with tens of NPUs. TACOS can synthesize for 40K NPUs in just 2.52 hours.

LGAug 21, 2023
Improving Clinical Decision Support through Interpretable Machine Learning and Error Handling in Electronic Health Records

Mehak Arora, Hassan Mortagy, Nathan Dwarshuis et al.

The objective of this work is to develop an Electronic Medical Record (EMR) data processing tool that confers clinical context to Machine Learning (ML) algorithms for error handling, bias mitigation and interpretability. We present Trust-MAPS, an algorithm that translates clinical domain knowledge into high-dimensional, mixed-integer programming models that capture physiological and biological constraints on clinical measurements. EMR data is projected onto this constrained space, effectively bringing outliers to fall within a physiologically feasible range. We then compute the distance of each data point from the constrained space modeling healthy physiology to quantify deviation from the norm. These distances, termed "trust-scores," are integrated into the feature space for downstream ML applications. We demonstrate the utility of Trust-MAPS by training a binary classifier for early sepsis prediction on data from the 2019 PhysioNet Computing in Cardiology Challenge, using the XGBoost algorithm and applying SMOTE for overcoming class-imbalance. The Trust-MAPS framework shows desirable behavior in handling potential errors and boosting predictive performance. We achieve an AUROC of 0.91 (0.89, 0.92 : 95% CI) for predicting sepsis 6 hours before onset - a marked 15% improvement over a baseline model trained without Trust-MAPS. Trust-scores emerge as clinically meaningful features that not only boost predictive performance for clinical decision support tasks, but also lend interpretability to ML models. This work is the first to translate clinical domain knowledge into mathematical constraints, model cross-vital dependencies, and identify aberrations in high-dimensional medical data. Our method allows for error handling in EMR, and confers interpretability and superior predictive power to models trained for clinical decision support.

44.4QUANT-PHApr 7
Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations

Jai Moondra, Philip C. Lotshaw, Greg Mohler et al.

We develop new approximate compilation schemes that significantly reduce the expense of compiling the Quantum Approximate Optimization Algorithm (QAOA) for solving the Max-Cut problem. Our main focus is on compilation with trapped-ion simulators using Pauli-$X$ operations and all-to-all Ising Hamiltonian $H_\text{Ising}$ evolution generated by Molmer-Sorensen or optical dipole force interactions, though some of our results also apply to standard gate-based compilations. Our results are based on principles of graph sparsification and decomposition; the former reduces the number of edges in a graph while maintaining its cut structure, while the latter breaks a weighted graph into a small number of unweighted graphs. Though these techniques have been used as heuristics in various hybrid quantum algorithms, there have been no guarantees on their performance, to the best of our knowledge. This work provides the first provable guarantees using sparsification and decomposition to improve quantum noise resilience and reduce quantum circuit complexity. For quantum hardware that uses edge-by-edge QAOA compilations, sparsification leads to a direct reduction in circuit complexity. For trapped-ion quantum simulators implementing all-to-all $H_\text{Ising}$ pulses, we show that for a $(1-ε)$ factor loss in the Max-Cut approximation ($ε>0)$, our compilations improve the (worst-case) number of $H_\text{Ising}$ pulses from $O(n^2)$ to $O(n\log(n/ε))$ and the (worst-case) number of Pauli-$X$ bit flips from $O(n^2)$ to $O\left(\frac{n\log(n/ε)}{ε^2}\right)$ for $n$-node graphs. We demonstrate significant reductions in noise are obtained in our new compilation approaches using theory and numerical calculations for trapped-ion hardware. We anticipate these approximate compilation techniques will be useful tools in a variety of future quantum computing experiments.

LGDec 7, 2022
Tree DNN: A Deep Container Network

Brijraj Singh, Swati Gupta, Mayukh Das et al.

Multi-Task Learning (MTL) has shown its importance at user products for fast training, data efficiency, reduced overfitting etc. MTL achieves it by sharing the network parameters and training a network for multiple tasks simultaneously. However, MTL does not provide the solution, if each task needs training from a different dataset. In order to solve the stated problem, we have proposed an architecture named TreeDNN along with it's training methodology. TreeDNN helps in training the model with multiple datasets simultaneously, where each branch of the tree may need a different training dataset. We have shown in the results that TreeDNN provides competitive performance with the advantage of reduced ROM requirement for parameter storage and increased responsiveness of the system by loading only specific branch at inference time.

OCFeb 13
Improved Regret Guarantees for Online Mirror Descent using a Portfolio of Mirror Maps

Swati Gupta, Jai Moondra, Mohit Singh

OMD and its variants give a flexible framework for OCO where the performance depends crucially on the choice of the mirror map. While the geometries underlying OPGD and OEG, both special cases of OMD, are well understood, it remains a challenging open question on how to construct an optimal mirror map for any given constrained set and a general family of loss functions, e.g., sparse losses. Motivated by parameterizing a near-optimal set of mirror maps, we consider a simpler question: is it even possible to obtain polynomial gains in regret by using mirror maps for geometries that interpolate between $L_1$ and $L_2$, which may not be possible by restricting to only OEG ($L_1$) or OPGD ($L_2$). Our main result answers this question positively. We show that mirror maps based on block norms adapt better to the sparsity of loss functions, compared to previous $L_p$ (for $p \in [1, 2]$) interpolations. In particular, we construct a family of online convex optimization instances in $\mathbb{R}^d$, where block norm-based mirror maps achieve a provable polynomial (in $d$) improvement in regret over OEG and OPGD for sparse loss functions. We then turn to the setting in which the sparsity level of the loss functions is unknown. In this case, the choice of geometry itself becomes an online decision problem. We first show that naively switching between OEG and OPGD can incur linear regret, highlighting the intrinsic difficulty of geometry selection. To overcome this issue, we propose a meta-algorithm based on multiplicative weights that dynamically selects among a family of uniform block norms. We show that this approach effectively tunes OMD to the sparsity of the losses, yielding adaptive regret guarantees. Overall, our results demonstrate that online mirror-map selection can significantly enhance the ability of OMD to exploit sparsity in online convex optimization.

25.3LGMay 7
Why Global LLM Leaderboards Are Misleading: Small Portfolios for Heterogeneous Supervised ML

Jai Moondra, Ayela Chughtai, Bhargavi Lanka et al.

Ranking LLMs via pairwise human feedback underpins current leaderboards for open-ended tasks, such as creative writing and problem-solving. We analyze ~89K comparisons in 116 languages from 52 LLMs from Arena, and show that the best-fit global Bradley-Terry (BT) ranking is misleading. Nearly 2/3 of the decisive votes cancel out, and even the top 50 models according to the global BT ranking are statistically indistinguishable (pairwise win probabilities are at most 0.53 within the top 50 models). We trace this failure to strong, structured heterogeneity of opinions across language, task, and time. Moreover, we find an important characteristic - *language* plays a key role. Grouping by language (and families) increases the agreement of votes massively, resulting in two orders of magnitude higher spread in the ELO scores (i.e., very consistent rankings). What appears as global noise is in fact a mixture of coherent but conflicting subpopulations. To address such heterogeneity in supervised machine learning, we introduce the framework of $(λ, ν)$-portfolios, which are small sets of models that achieve a prediction error at most $λ$, "covering" at least a $ν$ fraction of users. We formulate this as a variant of the set cover problem and provide guarantees using the VC dimension of the underlying set system. On the Arena data, our algorithms recover just 5 distinct BT rankings that cover over 96% of votes at a modest $λ$, compared to the 21% coverage by the global ranking. We also provide a portfolio of 6 LLMs that cover twice as many votes as the top-6 LLMs from a global ranking. We further construct portfolios for a classification problem on the COMPAS dataset using an ensemble of fairness-regularized classification models and show that these portfolios can be used to detect blind spots in the data, which might be of independent interest to policymakers.

46.9CLApr 5
Many Preferences, Few Policies: Towards Scalable Language Model Personalization

Cheol Woo Kum, Jai Moondra, Roozbeh Nahavandi et al.

The holy grail of LLM personalization is a single LLM for each user, perfectly aligned with that user's preferences. However, maintaining a separate LLM per user is impractical due to constraints on compute, memory, and system complexity. We address this challenge by developing a principled method for selecting a small portfolio of LLMs that captures representative behaviors across heterogeneous users. We model user preferences across multiple traits (e.g., safety, humor, brevity) through a multi-dimensional weight vector. Given reward functions across these dimensions, our algorithm PALM (Portfolio of Aligned LLMs) generates a small portfolio of LLMs such that, for any weight vector, the portfolio contains a near-optimal LLM for the corresponding scalarized objective. To the best of our knowledge, this is the first result that provides theoretical guarantees on both the size and approximation quality of LLM portfolios for personalization. It characterizes the trade-off between system cost and personalization, as well as the diversity of LLMs required to cover the landscape of user preferences. We provide empirical results that validate these guarantees and demonstrate greater output diversity over common baselines.

LGFeb 13, 2025
Navigating the Social Welfare Frontier: Portfolios for Multi-objective Reinforcement Learning

Cheol Woo Kim, Jai Moondra, Shresth Verma et al.

In many real-world applications of reinforcement learning (RL), deployed policies have varied impacts on different stakeholders, creating challenges in reaching consensus on how to effectively aggregate their preferences. Generalized $p$-means form a widely used class of social welfare functions for this purpose, with broad applications in fair resource allocation, AI alignment, and decision-making. This class includes well-known welfare functions such as Egalitarian, Nash, and Utilitarian welfare. However, selecting the appropriate social welfare function is challenging for decision-makers, as the structure and outcomes of optimal policies can be highly sensitive to the choice of $p$. To address this challenge, we study the concept of an $α$-approximate portfolio in RL, a set of policies that are approximately optimal across the family of generalized $p$-means for all $p \in [-\infty, 1]$. We propose algorithms to compute such portfolios and provide theoretical guarantees on the trade-offs among approximation factor, portfolio size, and computational efficiency. Experimental results on synthetic and real-world datasets demonstrate the effectiveness of our approach in summarizing the policy space induced by varying $p$ values, empowering decision-makers to navigate this landscape more effectively.

LGJun 22, 2021
Reusing Combinatorial Structure: Faster Iterative Projections over Submodular Base Polytopes

Jai Moondra, Hassan Mortagy, Swati Gupta

Optimization algorithms such as projected Newton's method, FISTA, mirror descent, and its variants enjoy near-optimal regret bounds and convergence rates, but suffer from a computational bottleneck of computing ``projections'' in potentially each iteration (e.g., $O(T^{1/2})$ regret of online mirror descent). On the other hand, conditional gradient variants solve a linear optimization in each iteration, but result in suboptimal rates (e.g., $O(T^{3/4})$ regret of online Frank-Wolfe). Motivated by this trade-off in runtime v/s convergence rates, we consider iterative projections of close-by points over widely-prevalent submodular base polytopes $B(f)$. We first give necessary and sufficient conditions for when two close points project to the same face of a polytope, and then show that points far away from the polytope project onto its vertices with high probability. We next use this theory and develop a toolkit to speed up the computation of iterative projections over submodular polytopes using both discrete and continuous perspectives. We subsequently adapt the away-step Frank-Wolfe algorithm to use this information and enable early termination. For the special case of cardinality-based submodular polytopes, we improve the runtime of computing certain Bregman projections by a factor of $Ω(n/\log(n))$. Our theoretical results show orders of magnitude reduction in runtime in preliminary computational experiments.

LGMar 16, 2021
Algorithmic Challenges in Ensuring Fairness at the Time of Decision

Jad Salem, Swati Gupta, Vijay Kamble

Algorithmic decision-making in societal contexts, such as retail pricing, loan administration, recommendations on online platforms, etc., can be framed as stochastic optimization under bandit feedback, which typically requires experimentation with different decisions for the sake of learning. Such experimentation often results in perceptions of unfairness among people impacted by these decisions; for instance, there have been several recent lawsuits accusing companies that deploy algorithmic pricing practices of price gouging. Motivated by the changing legal landscape surrounding algorithmic decision-making, we introduce the well-studied fairness notion of envy-freeness within the context of stochastic convex optimization. Our notion requires that upon receiving decisions in the present time, groups do not envy the decisions received by any of the other groups, both in the present as well as the past. This results in a novel trajectory-constrained stochastic optimization problem that renders existing techniques inapplicable. The main technical contribution of this work is to show problem settings where there is no gap in achievable regret (up to logarithmic factors) when envy-freeness is imposed. In particular, in our main result, we develop a near-optimal envy-free algorithm that achieves $\tilde{O}(\sqrt{T})$ regret for smooth convex functions that satisfy the PL inequality. This algorithm has a coordinate-descent structure, in which we carefully leverage gradient information to ensure monotonic sampling along each dimension, while avoiding overshooting the constrained optimum with high probability. This latter aspect critically uses smoothness and the structure of the envy-freeness constraints, while the PL inequality allows for sufficient progress towards the optimal solution. We discuss several open questions that arise from this analysis, which may be of independent interest.

CVJan 29, 2021
Multi-Threshold Attention U-Net (MTAU) based Model for Multimodal Brain Tumor Segmentation in MRI scans

Navchetan Awasthi, Rohit Pardasani, Swati Gupta

Gliomas are one of the most frequent brain tumors and are classified into high grade and low grade gliomas. The segmentation of various regions such as tumor core, enhancing tumor etc. plays an important role in determining severity and prognosis. Here, we have developed a multi-threshold model based on attention U-Net for identification of various regions of the tumor in magnetic resonance imaging (MRI). We propose a multi-path segmentation and built three separate models for the different regions of interest. The proposed model achieved mean Dice Coefficient of 0.59, 0.72, and 0.61 for enhancing tumor, whole tumor and tumor core respectively on the training dataset. The same model gave mean Dice Coefficient of 0.57, 0.73, and 0.61 on the validation dataset and 0.59, 0.72, and 0.57 on the test dataset.

OCJun 15, 2020
Walking in the Shadow: A New Perspective on Descent Directions for Constrained Minimization

Hassan Mortagy, Swati Gupta, Sebastian Pokutta

Descent directions such as movement towards Descent directions, including movement towards Frank-Wolfe vertices, away-steps, in-face away-steps and pairwise directions, have been an important design consideration in conditional gradient descent (CGD) variants. In this work, we attempt to demystify the impact of the movement in these directions towards attaining constrained minimizers. The optimal local direction of descent is the directional derivative (i.e., shadow) of the projection of the negative gradient. We show that this direction is the best away-step possible, and the continuous-time dynamics of moving in the shadow is equivalent to the dynamics of projected gradient descent (PGD), although it's non-trivial to discretize. We also show that Frank-Wolfe (FW) vertices correspond to projecting onto the polytope using an "infinite" step in the direction of the negative gradient, thus providing a new perspective on these steps. We combine these insights into a novel Shadow-CG method that uses FW and shadow steps, while enjoying linear convergence, with a rate that depends on the number of breakpoints in its projection curve, rather than the pyramidal width. We provide a linear bound on the number of breakpoints for simple polytopes and present scaling-invariant upper bounds for general polytopes based on the number of facets. We exemplify the benefit of using Shadow-CG computationally for various applications, while raising an open question about tightening the bound on the number of breakpoints for general polytopes.

LGJun 11, 2020
Group-Fair Online Allocation in Continuous Time

Semih Cayci, Swati Gupta, Atilla Eryilmaz

The theory of discrete-time online learning has been successfully applied in many problems that involve sequential decision-making under uncertainty. However, in many applications including contractual hiring in online freelancing platforms and server allocation in cloud computing systems, the outcome of each action is observed only after a random and action-dependent time. Furthermore, as a consequence of certain ethical and economic concerns, the controller may impose deadlines on the completion of each task, and require fairness across different groups in the allocation of total time budget $B$. In order to address these applications, we consider continuous-time online learning problem with fairness considerations, and present a novel framework based on continuous-time utility maximization. We show that this formulation recovers reward-maximizing, max-min fair and proportionally fair allocation rules across different groups as special cases. We characterize the optimal offline policy, which allocates the total time between different actions in an optimally fair way (as defined by the utility function), and impose deadlines to maximize time-efficiency. In the absence of any statistical knowledge, we propose a novel online learning algorithm based on dual ascent optimization for time averages, and prove that it achieves $\tilde{O}(B^{-1/2})$ regret bound.

CYApr 22, 2020
Reducing the Filtering Effect in Public School Admissions: A Bias-aware Analysis for Targeted Interventions

Yuri Faenza, Swati Gupta, Aapeli Vuorinen et al.

Problem definition: Traditionally, New York City's top 8 public schools have selected candidates solely based on their scores in the Specialized High School Admissions Test (SHSAT). These scores are known to be impacted by socioeconomic status of students and test preparation received in middle schools, leading to a massive filtering effect in the education pipeline. The classical mechanisms for assigning students to schools do not naturally address problems like school segregation and class diversity, which have worsened over the years. The scientific community, including policymakers, have reacted by incorporating group-specific quotas and proportionality constraints, with mixed results. The problem of finding effective and fair methods for broadening access to top-notch education is still unsolved. Methodology/results: We take an operations approach to the problem different from most established literature, with the goal of increasing opportunities for students with high economic needs. Using data from the Department of Education (DOE) in New York City, we show that there is a shift in the distribution of scores obtained by students that the DOE classifies as "disadvantaged" (following criteria mostly based on economic factors). We model this shift as a "bias" that results from an underestimation of the true potential of disadvantaged students. We analyze the impact this bias has on an assortative matching market. We show that centrally planned interventions can significantly reduce the impact of bias through scholarships or training, when they target the segment of disadvantaged students with average performance.

LGMay 26, 2019
Robust Classification using Robust Feature Augmentation

Kevin Eykholt, Swati Gupta, Atul Prakash et al.

Existing deep neural networks, say for image classification, have been shown to be vulnerable to adversarial images that can cause a DNN misclassification, without any perceptible change to an image. In this work, we propose shock absorbing robust features such as binarization, e.g., rounding, and group extraction, e.g., color or shape, to augment the classification pipeline, resulting in more robust classifiers. Experimentally, we show that augmenting ML models with these techniques leads to improved overall robustness on adversarial inputs as well as significant improvements in training time. On the MNIST dataset, we achieved 14x speedup in training time to obtain 90% adversarial accuracy com-pared to the state-of-the-art adversarial training method of Madry et al., as well as retained higher adversarial accuracy over a broader range of attacks. We also find robustness improvements on traffic sign classification using robust feature augmentation. Finally, we give theoretical insights for why one can expect robust feature augmentation to reduce adversarial input space

LGDec 10, 2018
Individual Fairness in Hindsight

Swati Gupta, Vijay Kamble

Since many critical decisions impacting human lives are increasingly being made by algorithms, it is important to ensure that the treatment of individuals under such algorithms is demonstrably fair under reasonable notions of fairness. One compelling notion proposed in the literature is that of individual fairness (IF), which advocates that similar individuals should be treated similarly (Dwork et al. 2012). Originally proposed for offline decisions, this notion does not, however, account for temporal considerations relevant for online decision-making. In this paper, we extend the notion of IF to account for the time at which a decision is made, in settings where there exists a notion of conduciveness of decisions as perceived by the affected individuals. We introduce two definitions: (i) fairness-across-time (FT) and (ii) fairness-in-hindsight (FH). FT is the simplest temporal extension of IF where treatment of individuals is required to be individually fair relative to the past as well as future, while in FH, we require a one-sided notion of individual fairness that is defined relative to only the past decisions. We show that these two definitions can have drastically different implications in the setting where the principal needs to learn the utility model. Linear regret relative to optimal individually fair decisions is inevitable under FT for non-trivial examples. On the other hand, we design a new algorithm: Cautious Fair Exploration (CaFE), which satisfies FH and achieves sub-linear regret guarantees for a broad range of settings. We characterize lower bounds showing that these guarantees are order-optimal in the worst case. FH can thus be embedded as a primary safeguard against unfair discrimination in algorithmic deployments, without hindering the ability to take good decisions in the long-run.

IRSep 11, 2016
E3 : Keyphrase based News Event Exploration Engine

Nikita Jain, Swati Gupta, Dhaval Patel

This paper presents a novel system E3 for extracting keyphrases from news content for the purpose of offering the news audience a broad overview of news events, with especially high content volume. Given an input query, E3 extracts keyphrases and enrich them by tagging, ranking and finding role for frequently associated keyphrases. Also, E3 finds the novelty and activeness of keyphrases using news publication date, to identify the most interesting and informative keyphrases.

LGMar 1, 2016
Solving Combinatorial Games using Products, Projections and Lexicographically Optimal Bases

Swati Gupta, Michel Goemans, Patrick Jaillet

In order to find Nash-equilibria for two-player zero-sum games where each player plays combinatorial objects like spanning trees, matchings etc, we consider two online learning algorithms: the online mirror descent (OMD) algorithm and the multiplicative weights update (MWU) algorithm. The OMD algorithm requires the computation of a certain Bregman projection, that has closed form solutions for simple convex sets like the Euclidean ball or the simplex. However, for general polyhedra one often needs to exploit the general machinery of convex optimization. We give a novel primal-style algorithm for computing Bregman projections on the base polytopes of polymatroids. Next, in the case of the MWU algorithm, although it scales logarithmically in the number of pure strategies or experts $N$ in terms of regret, the algorithm takes time polynomial in $N$; this especially becomes a problem when learning combinatorial objects. We give a general recipe to simulate the multiplicative weights update algorithm in time polynomial in their natural dimension. This is useful whenever there exists a polynomial time generalized counting oracle (even if approximate) over these objects. Finally, using the combinatorial structure of symmetric Nash-equilibria (SNE) when both players play bases of matroids, we show that these can be found with a single projection or convex minimization (without using online learning).