Novel framework for Bayesian reinforcement learning infers value function distributions.
problem Bayesian reinforcement learning's challenges in inferring value function distributions.
method Inferential Induction framework for Bayesian reinforcement learning, developing Bayesian Backwards Induction algorithm.
result Proposed algorithm is competitive with state-of-the-art methods.
A new approach uses backwards induction to accelerate reinforcement learning.
problem Training reinforcement learning agents to discover goals without supervision.
method Train model to predict backwards steps from known goal states.
result Empirically shows better performance than standard DDQN.
Method solves high-dimensional nonlinear PDEs using neural networks.
problem Solving high-dimensional fully nonlinear PDEs.
method Backward induction with multi-layer neural networks to estimate solution and its gradient, with Hessian approximated by automatic differentiation.
result Method extends previous work on semi-linear PDEs to fully nonlinear cases, demonstrating accuracy on various examples.
We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditional probability density function for the jump times and marks given t…
The study models financial derivatives with counterparty risk and corrects valuation methods.
problem Pricing financial derivatives considering counterparty credit risk and CVA.
method Developed a generic model for pricing derivatives with both unilateral and bilateral credit risks. Used backward induction for American style options. Emphasized that the market value is risky, not risk-free.
result Corrected the common mistake in the literature regarding the market value of defaultable derivatives.
Extends Bayesian OWL for multi-stage treatment decisions.
problem Lack of uncertainty quantification in treatment decisions.
method Backward Bayesian Outcome Weighted Learning (BBOWL).
result Propagates uncertainty backward through DTR learning process.
Method learns optimal treatment sequences from observational data.
problem Optimal dynamic treatment regimes for public policies and medical interventions.
method Doubly robust classification-based approach via backward induction.
result Achieves optimal convergence rate of n^(-1/2) for welfare regret.
New method uses reinforced regression for solving optimal stopping problems.
problem Solving optimal stopping problems in mathematical finance.
method Reinforced regression based on previously estimated continuation values.
result Illustrated by a numerical example from mathematical finance.
Deep learning schemes solve high-dimensional nonlinear PDEs and variational inequalities.
problem Solving high-dimensional nonlinear PDEs and variational inequalities.
method Machine learning using backward stochastic differential equations and deep neural networks.
result Deep learning schemes converge and give good results up to dimension 50.
GraphSAINT improves GCN training efficiency and accuracy with graph sampling.
problem Neighbor explosion problem in minibatch training of GCNs.
method GraphSAINT constructs minibatches by sampling the training graph, ensuring fixed well-connected nodes in all layers.
result GraphSAINT achieves new state-of-the-art F1 scores for PPI and Reddit.
Two neural network methods solve the master equation for MFGs.
problem Approximating Nash equilibria in stochastic, finite-agent games.
method Backward induction and direct PDE tackling neural networks.
result Neural networks can approximate the master equation's solution.
The paper analyzes stability and asymptotic behavior of hedging strategies in binomial and trinomial models.
problem Stability and asymptotic analysis of hedging strategies in incomplete financial models.
method Discrete-time Föllmer-Schweizer decomposition, perturbation analysis, and asymptotic approximation.
result Explicit formulas for leading order correction terms in asymptotic analysis.
Paper identifies reductive MDPs, solving them in polynomial time.
problem Computational hardness of general MDPs and tractability of finite-horizon MDPs.
method Defines reductivity, a new class of SSPs, and develops a polynomial-time solution.
result Optimal policies can be found in polynomial time for reductive SSPs and MDPs.
The paper analyzes trade execution strategies for large traders in a stochastic market environment.
problem Analyzing trade execution strategies in a stochastic market with price impact.
method Formulated a Markov game model and used backward induction method of dynamic programming.
result Explicit closed-form execution strategy at Markov perfect equilibrium.
New methods to define self-inductance by regularizing divergent integrals.
problem Defining self-inductance for identical loops.
method Regularization of divergent integrals using Neumann/Weber formula.
result Established new methods to calculate self-inductance.
Paper explores how knowledge distillation transfers inductive biases between models.
problem Transferring inductive biases between models for tasks with limited data.
method Knowledge distillation applied to models with different inductive biases (LSTMs vs. Transformers, CNNs vs. MLPs).
result Effect of inductive biases is transferred through knowledge distillation, impacting both performance and solution characteristics.
Interpolated-MLPs control inductive bias for better performance in low-compute tasks.
problem Low-compute performance gap between MLPs and CNNs.
method Introduced Interpolated MLP (I-MLP) approach to control inductive bias incrementally.
result Continuous logarithmic relationship between inductive bias and performance in low-compute tasks.
New method quantifies inductive bias for machine learning tasks.
problem Quantifying the amount of inductive bias in machine learning models.
method Estimates inductive bias by modeling loss distribution of random hypotheses.
result Higher dimensional tasks require greater inductive bias.
The paper develops methods to estimate optimal treatment sequences under policy constraints.
problem Estimating the best sequence of treatments over multiple stages for individuals.
method Empirical welfare maximization approach, solving treatment assignment sequentially or simultaneously.
result Established convergence rates and upper bounds for estimation methods.
Pricing Chinese convertible bonds using Monte Carlo simulation and dynamic programming.
problem Pricing Chinese convertible bonds accurately.
method Monte Carlo simulation and dynamic programming with regression and backward induction.
result An underpriced strategy significantly outperforms benchmarks.
One-layer transformers can't solve induction heads task efficiently.
problem Solving the induction heads task efficiently with one-layer transformers.
method Communication complexity argument showing exponential size requirement.
result No one-layer transformer can solve the induction heads task efficiently.
OTI extends OTP for inductive semi-supervised learning.
problem Inductive semi-supervised learning for out-of-sample data.
method Optimal transport-based approach extended to inductive tasks.
result OTI outperforms state-of-the-art methods in experiments.
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
problem Nonlinear Forward Backward Stochastic Differential Equations (FBSDE) with terminal conditions.
method Backward deep BSDE method applied to FBSDE with nonlinear generators and random initial conditions.
result Derives exact and Taylor-based approximations for time-stepping nonlinear BSDEs.
Strong inductive biases prevent harmless interpolation in overparameterized models.
problem Understanding the conditions under which overparameterized models can interpolate noise without overfitting.
method Theoretical analysis of high-dimensional kernel regression and deep neural networks, focusing on the role of inductive biases.
result The strength of an estimator's inductive bias determines whether interpolation is harmless or requires fitting noise for good generalization.
Deep ResNets favor low bottleneck rank with proper hyperparameters.
problem Understanding the inductive bias of deep neural networks.
method Computed minimum-norm weights of a deep linear ResNet.
result Deep nonlinear ResNets have an inductive bias towards minimizing bottleneck rank.
Decentralized learning achieves centralized performance via Gibbs measures.
problem Achieving centralized performance in decentralized machine learning.
method ERM-RER learning framework with Gibbs measures and relative-entropy regularization.
result Achieving centralized performance with Gibbs measures and specific scaling of regularization factors.
Improves sequence generation by training a backward network.
problem Generating long-term dependencies in sequence models.
method Train a backward recurrent network to predict states of a forward model.
result Achieves 9% relative improvement in speech recognition and significant improvement in caption generation.
This research formalizes inductive generalization and proposes a new learning paradigm called Inductive Learning.
problem Generalization from easy to hard tasks, especially out-of-domain generalization.
method Formalizes inductive generalization, introduces Inductive Learning, and outlines steps to adapt techniques for learning model successors.
result A new learning paradigm (Inductive Learning) that emphasizes induction and universal properties of learning and computation.
Shows uniqueness of mean curvature flow in higher dimensions.
problem Backwards uniqueness of mean curvature flow.
method Analysis of mean curvature flow with bounded second fundamental form.
result Proves backwards uniqueness in arbitrary codimension.
We introduce the notion of large scale inductive dimension for asymptotic resemblance spaces. We prove that the large scale inductive dimension and the asymptotic dimensiongrad are equal in the class of r-convex metric spaces. This class contains the class of all geodesic metric spaces and all finitely generated groups…
Unsupervised MT struggles with morphologically rich languages.
problem Limitations of unsupervised machine translation on morphologically rich languages.
method Adversarial unsupervised alignment of word embedding spaces for bilingual dictionary induction.
result A simple trick exploiting weak supervision from identical words improves unsupervised bilingual dictionary induction performance.
Paper studies forward-backward envelope for convex problems and applies it to least squares.
problem Minimizing the sum of a convex and a smooth function.
method Derives conditions for level-bounded and Kurdyka-Łojasiewicz functions, applies forward-backward envelope to difference-of-convex problems.
result Forward-backward envelope can be efficiently minimized for certain convex problems.
If p:Y→X is an unramified covering map between two compact oriented surfaces of genus at least two, then it is proved that the embedding map, corresponding to p, from the Teichmüller space T(X), for X, to T(Y) actually extends to an embedding between the Thurston compactification of the tw…
Backward exploration reduces sample complexity in policy evaluation.
problem Empirical policy evaluation in reinforcement learning.
method Backward exploration algorithms from high-cost states.
result Reduced average-case sample complexity to O(logS). Algorithm finds minimal colorings of tree structures.
problem Finding minimal unbounded factor complexity colorings of trees.
method Induction algorithm using colored balls.
result Characterization of Sturmian colorings.
Study eigenvalues of Laplace-Beltrami under Ricci flow on 3-manifolds.
problem Eigenvalue behavior under Ricci flow on 3-manifolds.
method Monotonic quantities and bounds constructed for the first eigenvalue.
result Eigenvalue tends to zero in converging cases after rescaling.
The study introduces backward baselines to distinguish past prediction from future prediction in machine learning models.
problem Differentiating between past and future prediction in machine learning models.
method Theoretical, empirical, and normative arguments support a family of simple and efficient statistical tests called backward baselines.
result The study provides a meaningful backward baseline for auditing black-box prediction systems.
Noise affects the effectiveness of interpolating models, especially those with strong inductive biases.
problem The impact of noise on interpolating models with strong inductive biases.
method Analyzing linear and classification models with sparse ground truths, proving fast rates for interpolators.
result Strong inductive biases can lead to faster but noisier interpolators, contrary to intuition.
We propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives. Our model extends the linearity-generating unspanned volatility term structure model by Carr et al. (2011) by a…
The paper extends NUP representations to factor graphs for better estimation.
problem Nontrivial model-based estimation problems.
method Augmenting factor graphs with convex-dual variables and NUP representations; proposing a new iterative algorithm.
result A new dual algorithm for state space problems.
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
Wavelets improve accuracy in solving backward SDEs.
problem Solving backward stochastic differential equations (SDEs) with high accuracy and simplicity.
method Time discretization combined with trigonometric wavelets, enhanced by antireflective boundary technique.
result Improved numerical algorithm for SDEs with enhanced accuracy and ease of implementation.
The paper derives upper hedging prices for multivariate contingent claims using game-theoretic probability and submodularity.
problem Deriving upper hedging prices for complex financial contracts.
method Game-theoretic approach, optimization over simplexes, Lovász extension, Black-Scholes-Barenblatt equations.
result Upper and lower hedging prices can be calculated efficiently for submodular or supermodular payoff functions.
GraIL predicts relations by reasoning over subgraphs, outperforming embeddings.
problem Relation prediction in knowledge graphs using latent representations is limited.
method Graph neural network with inductive bias to learn entity-independent relational semantics.
result GraIL outperforms existing rule-induction baselines in the inductive setting.
New approach relaxes inductive biases of physics-inspired NNs for better performance.
problem Challenges in applying physics-inspired NNs to real-world systems.
method Examined and relaxed inductive biases of Hamiltonian NNs, improving performance on non-conservative systems.
result Improved performance on practical, non-conservative systems by relaxing inductive biases.
IGMC learns inductive matrix completion without side info.
problem Inductive matrix completion without side information.
method Graph Neural Network (GNN) trained on 1-hop subgraphs of the rating matrix.
result Achieves competitive performance with state-of-the-art transductive baselines.
Paper presents IMRCs for evolving tasks with forward and backward learning.
problem Incremental learning of evolving tasks with few samples per task.
method Incremental minimax risk classifiers (IMRCs) that exploit forward and backward learning.
result IMRCs provide significant performance improvement, especially with reduced sample sizes.
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
problem Understanding how neural networks learn and generalize on Boolean data.
method End-to-end analysis of depth-2 discrete fully connected networks and DNF formulas, using Monte Carlo learning.
result Predictable training dynamics and interpretable features emerge, linking inductive bias and generalization.