Countless science and engineering applications in multi-objective optimization (MOO) necessitate that decision-makers (DMs) select a Pareto-optimal solution which aligns with their preferences. Evaluating individual solutions is often expensive, necessitating cost-sensitive optimization techniques. Due to competing objectives, the space of trade-offs is also expansive -- thus, examining the full Pareto frontier may prove overwhelming to a DM. Such real-world settings generally have loosely-defined and context-specific desirable regions for each objective function that can aid in constraining the search over the Pareto frontier. We introduce a novel conceptual framework that operationalizes these priors using soft-hard functions, SHFs, which allow for the DM to intuitively impose soft and hard bounds on each objective -- which has been lacking in previous MOO frameworks. Leveraging a novel minimax formulation for Pareto frontier sampling, we propose a two-step process for obtaining a compact set of Pareto-optimal points which respect the user-defined soft and hard bounds: (1) densely sample the Pareto frontier using Bayesian optimization, and (2) sparsify the selected set to surface to the user, using robust submodular function optimization. We prove that (2) obtains the optimal compact Pareto-optimal set of points from (1). We further show that many practical problems fit within the SHF framework and provide extensive empirical validation on diverse domains, including brachytherapy, engineering design, and large language model personalization. Specifically, for brachytherapy, our approach returns a compact set of points with over 3% greater SHF-defined utility than the next best approach. Among the other diverse experiments, our approach consistently leads in utility, allowing the DM to reach >99% of their maximum possible desired utility within validation of 5 points.

Proof-of-Learning (PoL) proposes that a model owner logs training checkpoints to establish a proof of having expended the computation necessary for training. The authors of PoL forego cryptographic approaches and trade rigorous security guarantees for scalability to deep learning. They empirically argued the benefit of this approach by showing how spoofing--computing a proof for a stolen model--is as expensive as obtaining the proof honestly by training the model. However, recent work has provided a counter-example and thus has invalidated this observation. In this work we demonstrate, first, that while it is true that current PoL verification is not robust to adversaries, recent work has largely underestimated this lack of robustness. This is because existing spoofing strategies are either unreproducible or target weakened instantiations of PoL--meaning they are easily thwarted by changing hyperparameters of the verification. Instead, we introduce the first spoofing strategies that can be reproduced across different configurations of the PoL verification and can be done for a fraction of the cost of previous spoofing strategies. This is possible because we identify key vulnerabilities of PoL and systematically analyze the underlying assumptions needed for robust verification of a proof. On the theoretical side, we show how realizing these assumptions reduces to open problems in learning theory.We conclude that one cannot develop a provably robust PoL verification mechanism without further understanding of optimization in deep learning.

Private multi-winner voting is the task of revealing $k$-hot binary vectors satisfying a bounded differential privacy (DP) guarantee. This task has been understudied in machine learning literature despite its prevalence in many domains such as healthcare. We propose three new DP multi-winner mechanisms: Binary, $\tau$, and Powerset voting. Binary voting operates independently per label through composition. $\tau$ voting bounds votes optimally in their $\ell_2$ norm for tight data-independent guarantees. Powerset voting operates over the entire binary vector by viewing the possible outcomes as a power set. Our theoretical and empirical analysis shows that Binary voting can be a competitive mechanism on many tasks unless there are strong correlations between labels, in which case Powerset voting outperforms it. We use our mechanisms to enable privacy-preserving multi-label learning in the central setting by extending the canonical single-label technique: PATE. We find that our techniques outperform current state-of-the-art approaches on large, real-world healthcare data and standard multi-label benchmarks. We further enable multi-label confidential and private collaborative (CaPC) learning and show that model performance can be significantly improved in the multi-site setting.

Training machine learning (ML) models typically involves expensive iterative optimization. Once the model's final parameters are released, there is currently no mechanism for the entity which trained the model to prove that these parameters were indeed the result of this optimization procedure. Such a mechanism would support security of ML applications in several ways. For instance, it would simplify ownership resolution when multiple parties contest ownership of a specific model. It would also facilitate the distributed training across untrusted workers where Byzantine workers might otherwise mount a denial-of-service by returning incorrect model updates. In this paper, we remediate this problem by introducing the concept of proof-of-learning in ML. Inspired by research on both proof-of-work and verified computations, we observe how a seminal training algorithm, stochastic gradient descent, accumulates secret information due to its stochasticity. This produces a natural construction for a proof-of-learning which demonstrates that a party has expended the compute require to obtain a set of model parameters correctly. In particular, our analyses and experiments show that an adversary seeking to illegitimately manufacture a proof-of-learning needs to perform *at least* as much work than is needed for gradient descent itself. We also instantiate a concrete proof-of-learning mechanism in both of the scenarios described above. In model ownership resolution, it protects the intellectual property of models released publicly. In distributed training, it preserves availability of the training procedure. Our empirical evaluation validates that our proof-of-learning mechanism is robust to variance induced by the hardware (ML accelerators) and software stacks.