Talks

In this work, we study structured multi-armed bandits, which is the problem of online decision-making under uncertainty in the presence of structural information. In this problem, the decision-maker needs to discover the best course of action despite observing only uncertain rewards over time. The decision-maker is aware of certain structural information regarding the reward distributions and would like to minimize their regret by exploiting this information, where the regret is its performance difference against a benchmark policy that knows the best action ahead of time. In the absence of structural information, the classical upper confidence bound (UCB) and Thomson sampling algorithms are well known to suffer only minimal regret. As recently pointed out, neither algorithms are, however, capable of exploiting structural information that is commonly available in practice. We propose a novel learning algorithm that we call DUSA whose worst-case regret matches the information-theoretic regret lower bound up to a constant factor and can handle a wide range of structural information. Our algorithm DUSA solves a dual counterpart of the regret lower bound at the empirical reward distribution and follows its suggested play. Our proposed algorithm is the first computationally viable learning policy for structured bandit problems that has asymptotic minimal regret.

Motivated by a variety of online matching markets, we consider demand and supply which arise i.i.d. in [0,1]^d, and need to be matched with each other while minimizing the expected average distance between matched pairs (the "cost"). We characterize the achievable cost scaling in three models as a function of the dimension d and the amount of excess supply (M or m): (i) Static matching of N demand units with N+M supply units. (ii) A semi-dynamic model where N+M supply units are present beforehand and N demand units arrive sequentially and must be matched immediately. (iii) A fully dynamic model where there are always m supply units present in the system, one supply and one demand unit arrive in each period, and the demand unit must be matched immediately. We show that, despite the matching constraint and uncertainty about the future, cost nearly as small as the distance to the nearest neighbor is achievable in all cases *except* models (i) and (ii) for d=1 and M = o(N). Moreover, the latter is the only case in models (i) and (ii) where excess supply significantly reduces the achievable cost. In papers with Omar Besbes, Akshit Kumar and Yilun Chen, we introduce application-inspired variants of model (ii) in which the distributions of supply and demand can be different, and generate new algorithmic and scaling insights. Links to papers: Paper 1, Paper 2 and Paper 3.  

The Entanglement Bootstrap is a program to derive the universal properties of a phase of matter from a single representative wavefunction on a topologically-trivial region.  Much (perhaps all) of the structure of topological quantum field theory can be extracted starting from a state satisfying two axioms that implement the area law for entanglement.  This talk will focus on recent progress (with Bowen Shi and Jin-Long Huang) using this approach to prove remote detectability of topological excitations in various dimensions.  This is an axiom of topological field theory.  Two key ideas are a quantum avatar of Kirby's torus trick to construct states on closed manifolds, and the new concept of pairing manifold, which is a closed manifold associated with a pair of conjugate excitation types that encodes their braiding matrix.  The pairing manifold also produces Verlinde formulae relating the S-matrix to the structure constants of a generalized symmetry algebra of flexible operators.  

Zoom link:  https://pitp.zoom.us/j/92633473610?pwd=eEhqR3BaQXljQm5ScHZvZm81N2FyZz09

The elementary CuO2 plane sustaining cuprate high temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO5 pyramids. Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate t/ℏ and across the charge-transfer energy gap E, generate ‘superexchange’ spin-spin interactions of energy J≈4t4/E3 in an antiferromagnetic correlated-insulator state. However, hole doping this CuO2 plane converts this into a very high temperature superconducting state whose electron-pairing is exceptional. A leading proposal for the mechanism of this intense electron-pairing is that, while hole doping destroys magnetic order it preserves pair-forming superexchange interactions governed by the charge-transfer energy scale E.

To explore this hypothesis directly at atomic-scale, we developed high-voltage single-electron and electron-pair (Josephson) scanning tunneling microscopy, to visualize the interplay of E and the electron-pair density nP in Bi2Sr2CaCu2O8+x. Changing the distance δ between each pyramid’s apical O atom and the CuO2 plane below, should alter the energy levels of the planar Cu and O orbitals and thus vary E.  Hence, the responses of both E and nP to alterations in δ that occur naturally in Bi2Sr2CaCu2O8+x were visualized. These data revealed, directly at atomic scale, the crux of strongly correlated superconductivity in CuO2: the response of the electron-pair condensate to varying the charge transfer energy. Strong concurrence between these observations and recent three-band Hubbard model DMFT predictions for superconductivity in hole-doped Bi2Sr2CaCu2O8+x (PNAS 118, e2106476118 (2021)) indicate that charge-transfer superexchange is the electron-pairing mechanism (PNAS 119, 2207449119 (2022)).

Zoom link:  https://pitp.zoom.us/j/95592484157?pwd=YU56Wno3WnBIUTlyaC9VSHJ3cGxZUT09

Online allocation problems with resource constraints are central problems in revenue management and online advertising. In these problems, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to choose an action that consumes a certain amount of resources and generates reward. The objective is to maximize cumulative rewards subject to a constraint on the total consumption of resources. In this talk, we consider a data-driven setting in which the reward and resource consumption of each request are generated using an input model that is unknown to the decision maker. We design a general class of algorithms that attain good performance in various input models without knowing which type of input they are facing. In particular, our algorithms are asymptotically optimal under independent and identically distributed inputs as well as various non-stationary stochastic input models, and they attain an asymptotically optimal fixed competitive ratio when the input is adversarial. Our algorithms operate in the Lagrangian dual space: they maintain a dual multiplier for each resource that is updated using online algorithms, such as, online mirror descent and PI controller. Our proposed algorithms are simple, fast, robust to estimation errors, and do not require convexity in the revenue function, consumption function and action space, in contrast to existing methods for online allocation problems. The major motivation of this line of research is the applications to budget pacing in online advertising.

We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like the Adwords problem, online stochastic packing and covering, online stochastic matching with concave returns, etc. form a special case of online stochastic CP. We present fast algorithms for these problems, which achieve near-optimal regret guarantees for both the i.i.d. and the random permutation models of stochastic inputs. When applied to the special case of online packing, our ideas yield a simpler and faster primal-dual algorithm for this well studied problem, which achieves the optimal competitive ratio. Our techniques make explicit the connection of primal-dual paradigm and online learning to online stochastic CP.

Tensor network provides a geometric representation of quantum many-body wave functions. Inspired by holography, we discuss a geometric realization of (one-shot) entanglement distillation for tensor networks including the multi-scale entanglement renormalization ansatz and matrix product states. We evaluate the trace distances between the ‘distilled' states and EPR states step by step and see a trend of distillation. If time permits, I will mention a possible field theoretic generalization of this geometric distillation.

Zoom link: https://pitp.zoom.us/j/98545776462?pwd=b1Z3ZENNRWVITlNOZG1GdzJaMmN1Zz09

Decision-makers often face the "many bandits" problem, where one must simultaneously learn across related but heterogeneous contextual bandit instances. For instance, a large retailer may wish to dynamically learn product demand across many stores to solve pricing or inventory problems, making it desirable to learn jointly for stores serving similar customers; alternatively, a hospital network may wish to dynamically learn patient risk across many providers to allocate personalized interventions, making it desirable to learn jointly for hospitals serving similar patient populations. Motivated by real datasets, we decompose the unknown parameter in each bandit instance into a global parameter plus a sparse instance-specific term. Then, we propose a novel two-stage estimator that exploits this structure in a sample-efficient way by using a combination of robust statistics (to learn across similar instances) and LASSO regression (to debias the results). We embed this estimator within a bandit algorithm, and prove that it improves asymptotic regret bounds in the context dimension; this improvement is exponential for data-poor instances. We further demonstrate how our results depend on the underlying network structure of bandit instances. Finally, we illustrate the value of our approach on synthetic and real datasets. Joint work with Kan Xu. Paper: https://arxiv.org/abs/2112.14233

Oftentimes, decisions involve multiple, possible conflicting rewards, or costs. For example, solving a problem faster may incur extra cost, or sacrifice safety. In cases like this, one possibility is to aim for decisions that maximize the value obtained from one of the reward functions, while keeping the value obtained from the other reward functions above some prespecified target values. Up to logarithmic factors, we resolve the optimal words-case sample complexity of finding solutions to such problems in the discounted MDP setting when a generative model of the MDP is available. While this is clearly an oversimplified problem, our analysis reveals an interesting gap between the sample complexity of this problem and the sample complexity of solving MDPs when the solver needs to return a solution which, with a prescribed probability, cannot violate the constraints. In the talk, I will explain the background of the problem, the origin of the gap, the algorithm that we know to achieve the near-optimal sample complexity, closing with some open questions. This is joint work with Sharan Vaswani and Lin F. Yang

 

Can degrees of freedom in the interior of black holes be responsible for the entropy-area law? If yes, what spacetime appears? In this talk, I answer these questions at the semi-classical level. Specifically, a black hole is considered as a bound state consisting of many semi-classical degrees of freedom which exist uniformly inside and have maximum gravity. The distribution of their information determines the interior metric through the semi-classical Einstein equation. Then, the interior is a continuous stacking of AdS_2 times S^2 without horizon or singularity and behaves like a local thermal state. Evaluating the entropy density from thermodynamic relations and integrating it over the interior volume, the area law is obtained with the factor 1/4 for any interior degrees of freedom. Here, the dynamics of gravity plays an essential role in changing the entropy from the volume law to the area law. This should help us clarify the holographic property of black-hole entropy. [arXiv: 2207.14274]

Zoom link: https://pitp.zoom.us/j/99386433635?pwd=VzlLV2U4T1ZOYmRVbG9YVlFIemVVZz09