arXiv subjects

Kanghoon Lee

Publications and source records attributed to Kanghoon Lee.

At least 37 records · Page 2Linked to original sources

arXiv2024

ELA: Exploited Level Augmentation for Offline Learning in Zero-Sum Games

Offline learning has become widely used due to its ability to derive effective policies from offline datasets gathered by expert demonstrators without interacting with the environment directly. Recent research has explored various ways to enhance offline learning efficiency by considering the characteristics (e.g., expertise level or multiple demonstrators) of the dataset. However, a different approach is necessary in the context of zero-sum games, where outcomes vary significantly based on the strategy of the opponent. In this study, we introduce a novel approach that uses unsupervised learning techniques to estimate the exploited level of each trajectory from the offline dataset of zero-sum games made by diverse demonstrators. Subsequently, we incorporate the estimated exploited level into the offline learning to maximize the influence of the dominant strategy. Our method enables interpretable exploited level estimation in multiple zero-sum games and effectively identifies dominant strategy data. Also, our exploited level augmented offline learning significantly enhances the original offline learning algorithms including imitation learning and offline reinforcement learning for zero-sum games.

cs.GT↗

arXiv2024

Perturbations of General Relativity to All Orders and the General $n^{\rm th}$ Order Terms

We derive all-order expressions for perturbations of the Einstein-Hilbert action and the Einstein equation with the general $n$-th order terms. To this end, we employ Cheung and Remmen's perturbation conventions both in tensor density and the usual metric tensor formalisms, including the Einstein-dilaton theory. Remarkably, we find minimal building blocks that generate the entire perturbations for each of our formulations. We show that the number of terms of perturbations grows linearly as the order of perturbations increases. We regard our results as the reference and discuss how to derive perturbations in other conventions from the reference. As a consistency check, we compute graviton scattering amplitudes using the perturbiner method based on the perturbative Einstein equation. Finally we discuss how to generalise the results to curved backgrounds and incorporate additional matter.

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arXiv2023

Interactive Autonomous Navigation with Internal State Inference and Interactivity Estimation

Deep reinforcement learning (DRL) provides a promising way for intelligent agents (e.g., autonomous vehicles) to learn to navigate complex scenarios. However, DRL with neural networks as function approximators is typically considered a black box with little explainability and often suffers from suboptimal performance, especially for autonomous navigation in highly interactive multi-agent environments. To address these issues, we propose three auxiliary tasks with spatio-temporal relational reasoning and integrate them into the standard DRL framework, which improves the decision making performance and provides explainable intermediate indicators. We propose to explicitly infer the internal states (i.e., traits and intentions) of surrounding agents (e.g., human drivers) as well as to predict their future trajectories in the situations with and without the ego agent through counterfactual reasoning. These auxiliary tasks provide additional supervision signals to infer the behavior patterns of other interactive agents. Multiple variants of framework integration strategies are compared. We also employ a spatio-temporal graph neural network to encode relations between dynamic entities, which enhances both internal state inference and decision making of the ego agent. Moreover, we propose an interactivity estimation mechanism based on the difference between predicted trajectories in these two situations, which indicates the degree of influence of the ego agent on other agents. To validate the proposed method, we design an intersection driving simulator based on the Intelligent Intersection Driver Model (IIDM) that simulates vehicles and pedestrians. Our approach achieves robust and state-of-the-art performance in terms of standard evaluation metrics and provides explainable intermediate indicators (i.e., internal states, and interactivity scores) for decision making.

cs.RO↗

arXiv2023

Binary Black Holes and Quantum Off-Shell Recursion

The quantum off-shell recursion provides an efficient and universal computational tool for loop-level scattering amplitudes. In this work, we present a new comprehensive computational framework based on the quantum off-shell recursion for binary black hole systems. Using the quantum perturbiner method, we derive the recursions and solve them explicitly up to two-loop order. We develop a power-counting prescription that enables the straightforward separation of classical diagrams. We also devise a classification scheme that optimizes the integration by parts (IBP) reduction process, which makes higher-loop calculations more tractable. By employing the soft expansion technique, we remove irrelevant terms from the loop integrands and express them in terms of master integrals. We classify the one-loop and the two-loop classical diagrams, and their loop integrands are represented by linear combinations of the master integrals. Finally, we explicitly calculate the classical scalar 2 to 2 amplitudes in the potential region up to the 3PM order and reproduce the known results.

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arXiv2023

Robust Driving Policy Learning with Guided Meta Reinforcement Learning

Although deep reinforcement learning (DRL) has shown promising results for autonomous navigation in interactive traffic scenarios, existing work typically adopts a fixed behavior policy to control social vehicles in the training environment. This may cause the learned driving policy to overfit the environment, making it difficult to interact well with vehicles with different, unseen behaviors. In this work, we introduce an efficient method to train diverse driving policies for social vehicles as a single meta-policy. By randomizing the interaction-based reward functions of social vehicles, we can generate diverse objectives and efficiently train the meta-policy through guiding policies that achieve specific objectives. We further propose a training strategy to enhance the robustness of the ego vehicle's driving policy using the environment where social vehicles are controlled by the learned meta-policy. Our method successfully learns an ego driving policy that generalizes well to unseen situations with out-of-distribution (OOD) social agents' behaviors in a challenging uncontrolled T-intersection scenario.

cs.RO↗

arXiv2023

Poincaré generators at second post-Minkowskian order

We verify the global Poincaré invariance of the Hamiltonian mechanics of gravitating binary dynamics at the second post Minkowskian (2PM) order. For spinless point particles, based on the known 2PM Hamiltonian in the center of momentum frame, we compute the general 2PM Hamiltonian valid in an arbitrary reference frame. An off-shell extension of the 1PM Hamiltonian, which contributes at the 2PM order through an iteration process, plays a crucial role. We then construct the 2PM boost generator that uniquely satisfies all the conditions imposed by the Poincaré algebra.

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arXiv2022

The Off-Shell Recursion for Gravity and the Classical Double Copy for currents

We construct the off-shell recursion for gravity and the graviton current for the perturbative double field theory (DFT). We first formulate the perturbative DFT, which is equivalent but simpler to perturbative general relativity, to all-orders in fluctuations of generalised metric. The perturbative action and equations of motion (EoM) are derived to arbitrary order for pure gravity case. We then derive the graviton off-shell recursion, the gravity counterpart of the Berends-Giele recursion in Yang-Mills theory, through the so-called perturbiner method using the EoM of the perturbative DFT. We solve the recursion iteratively and obtain the graviton off-shell currents explicitly. We then discuss the classical double copy for the off-shell currents. We present the current KLT relation for gravity by extending the result proposed by Mizera and Skrzypek for the non-gravitational effective field theories. The relation represents graviton currents by squaring gluon currents with the KLT kernel up to gauge transformation and regular terms that do not have any pole. Finally we discuss the off-shell conservation of currents for nonlinear gauge choices.

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arXiv2022

Quantum Off-Shell Recursion Relation

We construct off-shell recursion relations for arbitrary loop-level scattering amplitudes beyond the conventional tree-level recursion relations for $ϕ^{4}$-theory and the Yang-Mills theory. We define a quantum perturbiner expansion that includes loop corrections from the quantum effective action formalism by identifying the external source. Our method clearly shows how the perturbiner expansion becomes an off-shell current generating function. Instead of using the classical equations of motion in the conventional perturbiner method, we exploit the Dyson-Schwinger equation to derive the quantum off-shell recursion relation to arbitrary order of loop-level scattering amplitudes. We solve the recursion relation and reproduce the results which agree up to one-loop six-point scattering amplitudes for $ϕ^{4}$-theory. Furthermore, we construct the recursions for computing loop-level correlation functions by replacing the choice of the external source.

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arXiv2022

Double copying Exceptional Field theories

We examine exceptional field theory through the lens of the generalised double copy formalism. This allows us to construct classical solutions in M-theory using a generalised Kerr-Schild ansatz and along the way indicates hints towards a single copy of M-theory. Based on a talk at the Nankai Symposium given by DSB.

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arXiv2021

Emergent dual holographic description as a non-perturbative generalization of the Wilsonian renormalization group

In holographic duality, dynamics along the emergent extra-dimensional space describes a renormalization group (RG) flow of the corresponding quantum field theory (QFT). Following this idea, we develop an emergent holographic description of a QFT, where not only the information of the RG flow is introduced into an IR holographic dual effective field theory (HDEFT), but also the UV information of the QFT is encoded in the HDEFT through the IR boundary condition. In particular, we argue that this dual holographic construction is self-consistent within the assumption of bulk locality, showing the following two aspects: The solution of the Hamilton-Jacobi equation is given by the IR boundary effective action, and the Ward identity involving the QFT energy-momentum tensor current is satisfied naturally. We discuss the role of the RG $β$-function in the bulk effective dynamics of the metric tensor near a conformally invariant fixed point. We claim that this emergent dual gravity theory generalizes the perturbative Wilsonian RG framework into a non-perturbative way.

hep-th↗

arXiv2021

The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory

We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supergravity (with manifest $SL(2)$ symmetry).

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arXiv2021

The Classical Double Copy for Half-Maximal Supergravities and T-duality

We study the classical double copy for ungauged half-maximal supergravities using the Kaluza-Klein reduction of double field theory (DFT). We construct a general formula for the Kaluza-Klein (KK) reduction of the DFT Kerr-Schild ansatz. The KK reduction of the ansatz is highly nonlinear, but the associated equations of motion are linear. This linear structure implies that half-maximal supergravities admit a classical double copy. We show that their single copy is given by a pair of Maxwell-scalar theories, which are the KK reduction of a higher-dimensional single copy of DFT. We also investigate their T-duality transformations - both the Buscher rule and continuous O(D,D) rotations. Applying the Buscher rule to the Kerr BH, we obtain a solution with a nontrivial Kalb-Ramond field and dilaton. We also identify the single copy of Sen's heterotic BH and the chiral null model and show that the chiral null model is self-dual under T-duality rotations.

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arXiv2020

The Classical Double Copy of a Point Charge

The classical double copy relates solutions to the equations of motion in gauge theory and in gravity. In this paper, we present two double-copy formalisms for relating the Coulomb solution in gauge theory to the two-parameter Janis-Newman-Winicour solution in gravity. The latter is a static, spherically symmetric, asymptotically flat solution that generically includes a dilaton field, but also admits the Schwarzschild solution as a special case. We first present the classical double copy as a perturbative construction, similar to its formulation for scattering amplitudes, and then present it as an exact map, with a novel generalisation of the Kerr-Schild double copy motivated by double field theory. The latter formalism exhibits the relation between the Kerr-Schild classical double copy and the string theory origin of the double copy for scattering amplitudes.

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arXiv2019

Heterotic Kerr-Schild Double Field Theory and Classical Double Copy

We discuss the generalization of the Kerr-Schild (KS) formalism for general relativity and double field theory (DFT) to the heterotic DFT and supergravity. We first introduce a heterotic KS ansatz by introducing a pair of null O(d,d+G) generalized tangent vectors. The pair of null vectors are represented by a pair of d-dimensional vector fields, and one of the vector fields is not a null vector. This implies that the null property of the usual KS formalism, which plays a crucial role in linearizing the field equations, can be partially relaxed in a consistent way. We show that the equations of motion under the heterotic KS ansatz in a flat background can be reduced to linear equations. Using the heterotic KS equations, we establish the single and zeroth copy for heterotic supergravity and derive the Maxwell and Maxwell-scalar equations. This agrees with the KLT relation for heterotic string theory.

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arXiv2018

Stochastic Doubly Robust Gradient

When training a machine learning model with observational data, it is often encountered that some values are systemically missing. Learning from the incomplete data in which the missingness depends on some covariates may lead to biased estimation of parameters and even harm the fairness of decision outcome. This paper proposes how to adjust the causal effect of covariates on the missingness when training models using stochastic gradient descent (SGD). Inspired by the design of doubly robust estimator and its theoretical property of double robustness, we introduce stochastic doubly robust gradient (SDRG) consisting of two models: weight-corrected gradients for inverse propensity score weighting and per-covariate control variates for regression adjustment. Also, we identify the connection between double robustness and variance reduction in SGD by demonstrating the SDRG algorithm with a unifying framework for variance reduced SGD. The performance of our approach is empirically tested by showing the convergence in training image classifiers with several examples of missing data.

cs.LG↗

arXiv2018

Kerr-Schild Double Field Theory and Classical Double Copy

The Kerr-Schild (KS) formalism is a powerful tool for constructing exact solutions in general relativity. In this paper, we present a generalization of the conventional KS formalism to double field theory (DFT) and supergravities. We introduce a generalized KS ansatz for the generalized metric in terms of a pair of null vectors. Applying this ansatz to the equations of motion of DFT, we construct the generalized KS field equation. While the generalized KS equations are quadratic in the fields, we show that it is possible to find solutions by considering linear equations only. Furthermore, we construct a Killing spinor equation under the generalized KS ansatz. Based on this formalism, we show that the classical double copy structure, which represents solutions of the Einstein equation in terms of solutions of the Maxwell equation, can be extended to the entire massless string NS-NS sector. We propose a supersymmetric classical double copy which shows that solutions of the Killing spinor equation can be realized in terms of solutions of the BPS equation of the supersymmetric Maxwell theory.

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arXiv2018

A Note on Circle Compactification of Tensile Ambitwistor String

We discuss a number of problems associated with the circle compactification of the bosonic tensile ambitwistor string with the asymmetric vacuum choice. By considering the spectrum and physical state conditions, we show that the circle radius plays a role as a tuning parameter which determines the low energy effective field theory. At the self dual point, we construct the current operators and compute OPEs between them. While the final outcome remains as yet inconclusive, several new results are obtained. Through the current algebra analysis we show that there is a subsector of the massless states where the gauge symmetry is enhanced to $ISO(2)_L\times SU(2)_R$. Using the fact that the one loop partition function is not modular invariant, we show that tensile ambitwistor string partition function is exactly the same as a field theory partition function. Our result proves that despite the existence of winding modes, which is a typical characteristic of a string, the tensile ambitwistor string behaves as a point particle theory.

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arXiv2017

A String Theory Which Isn't About Strings

Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct {\sl ab initio} quantized bosonic string theory with left-right asymmetric worldsheet vacuum and explore its consequences and implications. We critically examine the validity of new vacuum and carry out first-quantization using standard operator formalism. Remarkably, the string spectrum consists only of a finite number of degrees of freedom: string gravity (massless spin-two, Kalb-Ramond and dilaton fields) and two massive spin-two Fierz-Pauli fields. The massive spin-two fields have negative norm, opposite mass-squared, and provides a Lee-Wick type extension of string gravity. We compute two physical observables: tree-level scattering amplitudes and one-loop cosmological constant. Scattering amplitude of four dilatons is shown to be a rational function of kinematic invariants, and in $D=26$ factorizes into contributions of massless spin-two and a pair of massive spin-two fields. The string one loop partition function is shown to perfectly agree with one loop Feynman diagram of string gravity and two massive spin-two fields. In particular, it does not exhibit modular invariance. We critically compare our construction with recent studies and contrast differences.

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