We reconsider the problem of optimal trading in the presence of linear and quadratic costs, for arbitrary linear costs but in the limit where quadratic costs are small. Using matched asymptotic expansion techniques, we find that the trading speed vanishes inside a band that is narrower than in the absence of quadratic …
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
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48 results for “Linear cost”
Efficient algorithm for unknown linear systems with convex costs.
problem Controlling an unknown linear system with stochastic convex costs.
method Optimism in the Face of Uncertainty paradigm.
result Achieves optimal regret-rate.
The Thermodynamic Costs of Simple Linear Regressioncond-mat.stat-mech
Study on thermodynamic costs of simple linear regression.
problem Understanding thermodynamic costs in machine learning models.
method Approximated thermodynamic lower bounds for exact and stochastic linear regression.
result Derived scaling laws for optimal dataset size based on generalization error.
New algorithm controls linear systems with bandit feedback, achieving optimal regret.
problem Controlling linear systems with bandit feedback under adversarial costs.
method Developed a new algorithm for linear control with memory optimization technique.
result Achieved optimal regret growth proportional to square root of time horizon.
Paper optimizes broker performance by estimating execution costs.
problem Minimizing execution costs for large trades.
method Intraday modeling of execution cost components (linear and quadratic).
result Substantial improvements in estimating execution costs.
Paper presents an efficient algorithm for linear MDP with low switching cost.
problem Large state space reinforcement learning problems with low switching cost.
method First algorithm for linear MDP with low switching cost, achieving near-optimal regret and switching cost.
result Regret bound of $\widetilde{O}\left(\sqrt{d^3H^4K}
ight)$ and near-optimal switching cost of $O\left(d H\log K
ight)$.
In this short note, we consider mean-variance optimized portfolios with transaction costs. We show that introducing quadratic transaction costs makes the optimization problem more difficult than using linear transaction costs. The reason lies in the specification of the budget constraint, which is no longer linear. We …
New algorithm reduces switching costs in RL beyond linear MDPs.
problem Costly policy switching in reinforcement learning.
method ELEANOR-LowSwitching algorithm for linear Bellman-complete MDPs.
result Achieves near-optimal regret with logarithmic switching cost.
Linear cost and exponentially convergent approximation of Gaussian Matérn processes on intervalsmath.ST
Linear cost method approximates Gaussian Matérn processes with exponentially convergent accuracy.
problem High computational cost for Gaussian process inference and prediction.
method Optimal rational approximation of spectral density for Gaussian processes on bounded intervals.
result Exponential decrease in covariance error with increasing order of approximation.
Optimal algorithms for non-linear ridge bandits reduce burn-in cost.
problem Non-linear models introduce a burn-in period with fixed cost.
method Two-stage algorithm: find initial action, then treat locally linear.
result Two-stage algorithm is statistically optimal.
Optimal control in changing systems without strong convexity assumptions.
problem Adversarial changes in convex costs for unknown linear systems.
method Non-convex lower confidence bounds and computationally-efficient regret minimization.
result Achieves -regret rate, optimal compared to best stabilizing controller.
Federated Q-Learning achieves linear regret speedup with low communication cost.
problem Achieving linear regret speedup in federated reinforcement learning without high communication costs.
method Proposed two federated Q-Learning algorithms: FedQ-Hoeffding and FedQ-Bernstein, using event-triggered synchronization, novel step size selection, and concentration inequalities.
result Total regrets achieve linear speedup compared to single-agent counterparts with logarithmic communication cost.
A new method matches measures across different spaces using cost-regularized optimal transport.
problem Matching measures in different spaces without aligned data.
method Cost-regularized optimal transport formulation to match measures across two Euclidean spaces.
result Demonstrated applicability to single-cell spatial transcriptomics/multiomics matching tasks.
A distributed algorithm reduces communication cost in linear bandits to near-optimal levels.
problem Cooperative linear bandit optimization with stochastic contexts.
method DisBE-LUCB algorithm, DecBE-LUCB algorithm, sharing information through a central server or immediate neighbors.
result Communication cost of DisBE-LUCB matches information-theoretic lower bound up to logarithmic factors.
We consider a market consisting of one safe and one risky asset, which offer constant investment opportunities. Taking into account both proportional transaction costs and linear price impact, we derive optimal rebalancing policies for representative investors with constant relative risk aversion and a long horizon.
Linear classifier, least-squares cost function, and outliersphysics.data-an
A set of introductory notes on the subject of data classification using a linear classifier and least-squares cost function, and the negative effect of the presence of outliers on the decision boundary of the linear discriminant. We also show how a simple scaling could make the outlier less significant, thereby obtaini…
Paper tackles online control of linear systems with unbounded noise.
problem Online control of linear systems under unbounded noise with unknown convex cost functions.
method Developed an algorithm achieving high-probability regret under unbounded noise, and established regret bound for strongly convex costs and sub-Gaussian noise.
result Achieved high-probability regret under unbounded noise, and regret bound for specific noise and cost conditions.
In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node up…
Framework learns linear programs from optimal decisions.
problem Learning linear programs from optimal decisions is challenging.
method Gradient-based framework for learning linear programs from optimal decisions.
result Successfully learns linear programs and multi-commodity flow instances.
Study learns state representations from observations for control, proving guarantees.
problem Learning state representations from high-dimensional observations for control.
method Cost-driven approach, learning latent state model to predict costs.
result Proves finite-sample guarantees for near-optimal state representation and controller.
New algorithm reduces regret in linear mixture SSPs without cost bounds.
problem Learning optimal paths in stochastic environments with cost constraints.
method Extended value iteration with variance-aware confidence set.
result Achieves nearly minimax optimal regret bound of .
A method for pricing and superhedging European options under proportional transaction costs based on linear vector optimisation and geometric duality developed by Lohne & Rudloff (2014) is compared to a special case of the algorithms for American type derivatives due to Roux & Zastawniak (2014). An equivalence between …
New trading policies preserve robust gains in presence of transaction costs.
problem Maintaining robust gains in asset trading with transaction costs.
method Proposed double linear trading policies, analyzed with Monte Carlo simulations and historical data.
result Desired robust positive expected gain can be preserved under certain conditions.
Adaptive policies solve a linear program to maximize rewards while minimizing costs in sales with discounts.
problem Maximizing rewards in sales with discounts while considering costs.
method Solves a linear program based on upper-confidence estimates of conversion probabilities.
result Achieves a regret bound of the typical order (OPT/) , where B is the total budget allowed.
Study cost-driven state representation learning for control from partial observations.
problem Learning state representation for control from partial and high-dimensional observations.
method Cost-driven state representation learning via predicting cumulative costs.
result Established finite-sample guarantees for near-optimal representation and controller.
The paper presents efficient methods for identifying causal graphs with latent variables.
problem Recovering causal graphs with latent variables while minimizing intervention costs.
method Two intervention cost models (linear and identity) are considered. Algorithms are provided for both models.
result Upper bounds on the number of interventions needed for recovery, and approximation factors for the linear cost model.
Solves steering problem with continuous time, Hilbert-Schmidt cost, and matrix ODEs.
problem Fixed horizon linear quadratic covariance steering in continuous time with a specific terminal cost.
method Formulates necessary conditions as a coupled matrix ODE two-point boundary value problem, designs a matricial recursive algorithm, and proves convergence.
result Proposes and proves the convergence of a matricial recursive algorithm for solving the steering problem.
LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.
problem Computational bottleneck in randomization step for large-scale linear algebra.
method Near constant-time linear random projections from LightOn OPUs.
result Significant acceleration of RandNLA algorithms with negligible precision loss.
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
New algorithms for planning with adversarial changes in costs.
problem Planning with adversarial changes in costs over time.
method Developed algorithms for adversarial SSP with high probability regret bounds.
result Obtained sub-linear regret bounds for adversarial SSP.
Projection-cost preservation is a low-rank approximation guarantee which ensures that the cost of any rank- projection can be preserved using a smaller sketch of the original data matrix. We present a general structural result outlining four sufficient conditions to achieve projection-cost preservation. These condit…
Designs a neural network to reduce training cost by mapping to higher dimensions.
problem High training cost in neural networks.
method Maps feature vectors to higher dimensional space, designs weight matrices to reduce cost, uses convex constraints.
result Reduces training cost as the number of layers increases, without cross-validation.
OMGD algorithm optimizes online convex optimization with switching costs and delayed gradients.
problem Optimizing online convex optimization with switching costs and delayed gradients.
method Proposed an online multiple gradient descent (OMGD) algorithm for quadratic and linear switching costs.
result OMGD achieves optimal dynamic regret in the limited information setting.
New method disentangles perceptual uncertainty and behavioral costs in partially observable systems.
problem Tackles inverse optimal control for non-linear partially observable systems.
method Probabilistic approach using maximum causal entropy formulations and local linearization.
result Disentangles perceptual factors and behavioral costs in sequential decision-making.
We propose an algorithm for exploring the entire regularization path of asymmetric-cost linear support vector machines. Empirical evidence suggests the predictive power of support vector machines depends on the regularization parameters of the training algorithms. The algorithms exploring the entire regularization path…
New method speeds up change-point detection in data sequences.
problem Efficiently detecting change-points in long data sequences.
method Sequential Gradient Descent and Quasi-Newton's Method.
result New method can be orders of magnitude faster than existing methods.
We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-nega…
Study how transaction costs impact stock returns and holdings in equilibrium.
problem Impact of quadratic transaction costs on equilibrium stock returns and holdings.
method Developed a continuous-time risk-sharing model with FBSDEs to characterize equilibrium stock holdings and trading rates.
result Equilibrium stock holdings and trading rates are uniquely determined by FBSDEs, and equilibrium return by a system of coupled FBSDEs.
This paper concerns the problem of learning control policies for an unknown linear dynamical system to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task robustly: i.e., we minimize the worst-case cost, accounting for system uncertainty given the observed …
Proposes cost-sensitive feature selection for SVMs.
problem Asymmetric misclassification costs in feature selection.
method Mathematical optimization-based approach for SVMs.
result Substantial reduction in feature count with desired error rates.
Models of spatial firm competition assume that customers are distributed in space and transportation costs are associated with their purchases of products from a small number of firms that are also placed at definite locations. It has been long known that the competition equilibrium is not guaranteed to exist if the mo…
Agent optimizes perpetual contract liquidation with transaction costs and risk.
problem Optimizing perpetual contract liquidation with transaction costs and risk.
method Solving stochastic control problem for optimal trading strategy.
result Closed-form expression and approximations for optimal strategy.
An algorithm for maximizing rewards under linear cost constraints.
problem Maximizing rewards while adhering to cost constraints in a linear bandit problem.
method Proposes an upper-confidence bound algorithm called optimistic pessimistic linear bandit (OPLB) for constrained contextual linear bandits.
result Proves an bound on regret for the proposed algorithm.
Agents collaborate to minimize regret while keeping costs under a threshold.
problem Collaborative multi-agent stochastic linear bandits with cost constraints.
method Safe distributed upper confidence bound algorithm (MA-OPLB) with accelerated consensus.
result Regret bound of order $ \mathcal{O}\left(\frac{d}{τ-c_0}\frac{\log(NT)^2}{\sqrt{N}}\sqrt{\frac{T}{\log(1/|λ_2|)}}
ight)$.
Optimal liquidation model reduces trading costs in OTC markets.
problem Minimizing trading costs in Over-The-Counter markets.
method Developed an optimal portfolio liquidation model in Locally Linear Order Book framework.
result Optimal liquidation time is proportional to the square root of the traded volume.
Solves asset allocation for investors with utility functions and limits.
problem Investor risk and utility with position limits.
method Analytical solution for piecewise-linear utility function with position limits.
result Simple functional form representing risk cost.
SCaLE tackles dynamic regret in noisy bandit feedback with switching costs.
problem Unbounded metric movement costs in bandit online convex optimization.
method SCaLE algorithm for high-dimensional dynamic quadratic hitting costs and -norm switching costs, with spectral regret analysis.
result First algorithm achieving sub-linear dynamic regret without hitting cost knowledge.
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained optimization from theoretical, algorithmic, and application aspects in the context of spars…