We consider the Pareto set identification (PSI) problem in multi-objectivemulti-armed bandits (MO-MAB) with contaminated reward observations. At each armpull, with some fixed probability, the true reward samples are replaced withthe samples from an arbitrary contamination distribution chosen by anadversary. We consider ({\alpha}, {\delta})-PAC PSI and propose a samplemedian-based multi-objective adaptive elimination algorithm that returns an({\alpha}, {\delta})- PAC Pareto set upon termination with a sample complexitybound that depends on the contamination probability. As the contaminationprobability decreases, we recover the wellknown sample complexity results inMO-MAB. We compare the proposed algorithm with a mean-based method from MO-MABliterature, as well as an extended version that uses median estimators, onseveral PSI problems under adversarial corruptions, including review bombingand diabetes management. Our numerical results support our theoretical findingsand demonstrate that robust algorithm design is crucial for accurate PSI undercontaminated reward observations.
We address the problem of learning the legitimacy of other agents in amultiagent network when an unknown subset is comprised of malicious actors. Wespecifically derive results for the case of directed graphs and wherestochastic side information, or observations of trust, is available. We referto this as ``learning trust'' since agents must identify which neighbors in thenetwork are reliable, and we derive a protocol to achieve this. We also provideanalytical results showing that under this protocol i) agents can learn thelegitimacy of all other agents almost surely, and that ii) the opinions of theagents converge in mean to the true legitimacy of all other agents in thenetwork. Lastly, we provide numerical studies showing that our convergenceresults hold in practice for various network topologies and variations in thenumber of malicious agents in the network.
The slowing down of Moore's law has driven the development of unconventionalcomputing paradigms, such as specialized Ising machines tailored to solvecombinatorial optimization problems. In this paper, we show a new applicationdomain for probabilistic bit (p-bit) based Ising machines by training deepgenerative AI models with them. Using sparse, asynchronous, and massivelyparallel Ising machines we train deep Boltzmann networks in a hybridprobabilistic-classical computing setup. We use the full MNIST and FashionMNIST (FMNIST) dataset without any downsampling and a reduced version ofCIFAR-10 dataset in hardware-aware network topologies implemented in moderatelysized Field Programmable Gate Arrays (FPGA). For MNIST, our machine using only4,264 nodes (p-bits) and about 30,000 parameters achieves the sameclassification accuracy (90%) as an optimized software-based restrictedBoltzmann Machine (RBM) with approximately 3.25 million parameters. Similarresults follow for FMNIST and CIFAR-10. Additionally, the sparse deep Boltzmannnetwork can generate new handwritten digits and fashion products, a task the3.25 million parameter RBM fails at despite achieving the same accuracy. Ourhybrid computer takes a measured 50 to 64 billion probabilistic flips persecond, which is at least an order of magnitude faster than superficiallysimilar Graphics and Tensor Processing Unit (GPU/TPU) based implementations.The massively parallel architecture can comfortably perform the contrastivedivergence algorithm (CD-n) with up to n = 10 million sweeps per update, beyondthe capabilities of existing software implementations. These resultsdemonstrate the potential of using Ising machines for traditionallyhard-to-train deep generative Boltzmann networks, with further possibleimprovement in nanodevice-based realizations.
Biological and artificial information processing systems form representationsof the world that they can use to categorize, reason, plan, navigate, and makedecisions. How can we measure the similarity between the representations formedby these diverse systems? Do similarities in representations then translateinto similar behavior? If so, then how can a system's representations bemodified to better match those of another system? These questions pertaining tothe study of representational alignment are at the heart of some of the mostpromising research areas in contemporary cognitive science, neuroscience, andmachine learning. In this Perspective, we survey the exciting recentdevelopments in representational alignment research in the fields of cognitivescience, neuroscience, and machine learning. Despite their overlappinginterests, there is limited knowledge transfer between these fields, so work inone field ends up duplicated in another, and useful innovations are not sharedeffectively. To improve communication, we propose a unifying framework that canserve as a common language for research on representational alignment, and mapseveral streams of existing work across fields within our framework. We alsolay out open problems in representational alignment where progress can benefitall three of these fields. We hope that this paper will catalyzecross-disciplinary collaboration and accelerate progress for all communitiesstudying and developing information processing systems.