NeurIPS 2024 论文列表

Conference on Neural Information Processing Systems

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4,562篇论文

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    3828.4%
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    4,06489.1%
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Artificial Generational Intelligence: Cultural Accumulation in Reinforcement Learning

Jonathan Cook, Chris Lu, Edward Hughes, Joel Z Leibo, Jakob Nicolaus Foerster

展开摘要

Cultural accumulation drives the open-ended and diverse progress in capabilities spanning human history. It builds an expanding body of knowledge and skills by combining individual exploration with inter-generational information transmission. Despite its widespread success among humans, the capacity for artificial learning agents to accumulate culture remains under-explored. In particular, approaches to reinforcement learning typically strive for improvements over only a single lifetime. Generational algorithms that do exist fail to capture the open-ended, emergent nature of cultural accumulation, which allows individuals to trade-off innovation and imitation. Building on the previously demonstrated ability for reinforcement learning agents to perform social learning, we find that training setups which balance this with independent learning give rise to cultural accumulation. These accumulating agents outperform those trained for a single lifetime with the same cumulative experience. We explore this accumulation by constructing two models under two distinct notions of a generation: episodic generations, in which accumulation occurs via in-context learning and train-time generations, in which accumulation occurs via in-weights learning. In-context and in-weights cultural accumulation can be interpreted as analogous to knowledge and skill accumulation, respectively. To the best of our knowledge, this work is the first to present general models that achieve emergent cultural accumulation in reinforcement learning, opening up new avenues towards more open-ended learning systems, as well as presenting new opportunities for modelling human culture.

Poster
The Implicit Bias of Heterogeneity towards Invariance: A Study of Multi-Environment Matrix Sensing

Yang Xu, Yihong Gu, Cong Fang

展开摘要

Models are expected to engage in invariance learning, which involves distinguishing the core relations that remain consistent across varying environments to ensure the predictions are safe, robust and fair. While existing works consider specific algorithms to realize invariance learning, we show that model has the potential to learn invariance through standard training procedures. In other words, this paper studies the implicit bias of Stochastic Gradient Descent (SGD) over heterogeneous data and shows that the implicit bias drives the model learning towards an invariant solution. We call the phenomenon the implicit invariance learning. Specifically, we theoretically investigate the multi-environment low-rank matrix sensing problem where in each environment, the signal comprises (i) a lower-rank invariant part shared across all environments; and (ii) a significantly varying environment-dependent spurious component. The key insight is, through simply employing the large step size large-batch SGD sequentially in each environment without any explicit regularization, the oscillation caused by heterogeneity can provably prevent model learning spurious signals. The model reaches the invariant solution after certain iterations. In contrast, model learned using pooled SGD over all data would simultaneously learn both the invariant and spurious signals. Overall, we unveil another implicit bias that is a result of the symbiosis between the heterogeneity of data and modern algorithms, which is, to the best of our knowledge, first in the literature.

Poster
OT4P: Unlocking Effective Orthogonal Group Path for Permutation Relaxation

Yaming Guo, Chen Zhu, Hengshu Zhu, Tieru Wu

展开摘要

Optimization over permutations is typically an NP-hard problem that arises extensively in ranking, matching, tracking, etc. Birkhoff polytope-based relaxation methods have made significant advancements, particularly in penalty-free optimization and probabilistic inference. Relaxation onto the orthogonal group offers unique potential advantages such as a lower representation dimension and preservation of inner products; however, equally effective approaches remain unexplored. To bridge the gap, we present a temperature-controlled differentiable transformation that maps unconstrained vector space to the orthogonal group, where the temperature, in the limit, concentrates orthogonal matrices near permutation matrices. This transformation naturally implements a parameterization for the relaxation of permutation matrices, allowing for gradient-based optimization of problems involving permutations. Additionally, by deriving a re-parameterized gradient estimator, this transformation also provides efficient stochastic optimization over the latent permutations. Extensive experiments involving the optimization over permutation matrices validate the effectiveness of the proposed method.

Poster
Unleashing Multispectral Video's Potential in Semantic Segmentation: A Semi-supervised Viewpoint and New UAV-View Benchmark

Wei Ji, Jingjing Li, Wenbo Li, Yilin Shen, Li Cheng, Hongxia Jin

展开摘要

Thanks to the rapid progress in RGB & thermal imaging, also known as multispectral imaging, the task of multispectral video semantic segmentation, or MVSS in short, has recently drawn significant attentions. Noticeably, it offers new opportunities in improving segmentation performance under unfavorable visual conditions such as poor light or overexposure. Unfortunately, there are currently very few datasets available, including for example MVSeg dataset that focuses purely toward eye-level view; and it features the sparse annotation nature due to the intensive demands of labeling process. To address these key challenges of the MVSS task, this paper presents two major contributions: the introduction of MVUAV, a new MVSS benchmark dataset, and the development of a dedicated semi-supervised MVSS baseline - SemiMV. Our MVUAV dataset is captured via Unmanned Aerial Vehicles (UAV), which offers a unique oblique bird’s-eye view complementary to the existing MVSS datasets; it also encompasses a broad range of day/night lighting conditions and over 30 semantic categories. In the meantime, to better leverage the sparse annotations and extra unlabeled RGB-Thermal videos, a semi-supervised learning baseline, SemiMV, is proposed to enforce consistency regularization through a dedicated Cross-collaborative Consistency Learning (C3L) module and a denoised temporal aggregation strategy. Comprehensive empirical evaluations on both MVSeg and MVUAV benchmark datasets have showcased the efficacy of our SemiMV baseline.

Poster
The Limits of Transfer Reinforcement Learning with Latent Low-rank Structure

Tyler Sam, Yudong Chen, Christina Yu

展开摘要

Many reinforcement learning (RL) algorithms are too costly to use in practice due to the large sizes $S,A$ of the problem's state and action space. To resolve this issue, we study transfer RL with latent low rank structure. We consider the problem of transferring a latent low rank representation when the source and target MDPs have transition kernels with Tucker rank $(S, d, A)$, $(S ,S , d), (d, S , A )$, or $(d , d , d )$. In each setting, we introduce the transfer-ability coefficient $\alpha$ that measures the difficulty of representational transfer. Our algorithm learns latent representations in each source MDP and then exploits the linear structure to remove the dependence on $S , A $, or $SA $ in the target MDP regret bound. We complement our positive results with information theoretic lower bounds that show our algorithms (excluding the ($d, d, d$) setting) are minimax-optimal with respect to $\alpha$.

Poster
Scalable Constrained Policy Optimization for Safe Multi-agent Reinforcement Learning

Lijun Zhang, Lin Li, Wei Wei, Huizhong Song, Yaodong Yang, Jiye Liang

展开摘要

A challenging problem in seeking to bring multi-agent reinforcement learning (MARL) techniques into real-world applications, such as autonomous driving and drone swarms, is how to control multiple agents safely and cooperatively to accomplish tasks. Most existing safe MARL methods learn the centralized value function by introducing a global state to guide safety cooperation. However, the global coupling arising from agents’ safety constraints and the exponential growth of the state-action space size limit their applicability in instant communication or computing resource-constrained systems and larger multi-agent systems. In this paper, we develop a novel scalable and theoretically-justified multi-agent constrained policy optimization method. This method utilizes the rigorous bounds of the trust region method and the bounds of the truncated advantage function to provide a new local policy optimization objective for each agent. Also, we prove that the safety constraints and the joint policy improvement can be met when each agent adopts a sequential update scheme to optimize a $\kappa$-hop policy. Then, we propose a practical algorithm called Scalable MAPPO-Lagrangian (Scal-MAPPO-L). The proposed method’s effectiveness is verified on a collection of benchmark tasks, and the results support our theory that decentralized training with local interactions can still improve reward performance and satisfy safe constraints.

Poster
Make-An-Agent: A Generalizable Policy Network Generator with Behavior-Prompted Diffusion

Yongyuan Liang, Tingqiang Xu, Kaizhe Hu, Guangqi Jiang, Furong Huang, Huazhe Xu

展开摘要

Can we generate a control policy for an agent using just one demonstration of desired behaviors as a prompt, as effortlessly as creating an image from a textual description? In this paper, we present **Make-An-Agent**, a novel policy parameter generator that leverages the power of conditional diffusion models for behavior-to-policy generation. Guided by behavior embeddings that encode trajectory information, our policy generator synthesizes latent parameter representations, which can then be decoded into policy networks. Trained on policy network checkpoints and their corresponding trajectories, our generation model demonstrates remarkable versatility and scalability on multiple tasks and has a strong generalization ability on unseen tasks to output well-performed policies with only few-shot demonstrations as inputs. We showcase its efficacy and efficiency on various domains and tasks, including varying objectives, behaviors, and even across different robot manipulators. Beyond simulation, we directly deploy policies generated by **Make-An-Agent** onto real-world robots on locomotion tasks. Project page: https://cheryyunl.github.io/make-an-agent/.

Poster
Refusal in Language Models Is Mediated by a Single Direction

Andy Arditi, Oscar Balcells Obeso, Aaquib Syed, Daniel Paleka, Nina Rimsky, Wes Gurnee, Neel Nanda

展开摘要

Conversational large language models are fine-tuned for both instruction-following and safety, resulting in models that obey benign requests but refuse harmful ones. While this refusal behavior is widespread across chat models, its underlying mechanisms remain poorly understood. In this work, we show that refusal is mediated by a one-dimensional subspace, across 13 popular open-source chat models up to 72B parameters in size. Specifically, for each model, we find a single direction such that erasing this direction from the model's residual stream activations prevents it from refusing harmful instructions, while adding this direction elicits refusal on even harmless instructions. Leveraging this insight, we propose a novel white-box jailbreak method that surgically disables a model's ability to refuse, with minimal effect on other capabilities. This interpretable rank-one weight edit results in an effective jailbreak technique that is simpler and more efficient than fine-tuning. Finally, we mechanistically analyze how adversarial suffixes suppress propagation of the refusal-mediating direction. Our findings underscore the brittleness of current safety fine-tuning methods. More broadly, our work showcases how an understanding of model internals can be leveraged to develop practical methods for controlling model behavior.

Poster
Speculative Decoding with CTC-based Draft Model for LLM Inference Acceleration

Zhuofan Wen, Shangtong Gui, Yang Feng

展开摘要

Inference acceleration of large language models (LLMs) has been put forward in many application scenarios and speculative decoding has shown its advantage in addressing inference acceleration. Speculative decoding usually introduces a draft model to assist the base LLM where the draft model produces drafts and the base LLM verifies the draft for acceptance or rejection. In this framework, the final inference speed is decided by the decoding speed of the draft model and the acceptance rate of the draft provided by the draft model. Currently the widely used draft models usually generate draft tokens for the next several positions in a non-autoregressive way without considering the correlations between draft tokens. Therefore, it has a high decoding speed but an unsatisfactory acceptance rate. In this paper, we focus on how to improve the performance of the draft model and aim to accelerate inference via a high acceptance rate. To this end, we propose a CTC-based draft model which strengthens the correlations between draft tokens during the draft phase, thereby generating higher-quality draft candidate sequences. Experiment results show that compared to strong baselines, the proposed method can achieve a higher acceptance rate and hence a faster inference speed.

Poster
Learning on Large Graphs using Intersecting Communities

Ben Finkelshtein, Ismail Ilkan Ceylan, Michael M. Bronstein, Ron Levie

展开摘要

Message Passing Neural Networks (MPNNs) are a staple of graph machine learning. MPNNs iteratively update each node’s representation in an input graph by aggregating messages from the node’s neighbors, which necessitates a memory complexity of the order of the __number of graph edges__. This complexity might quickly become prohibitive for large graphs provided they are not very sparse. In this paper, we propose a novel approach to alleviate this problem by approximating the input graph as an intersecting community graph (ICG) -- a combination of intersecting cliques. The key insight is that the number of communities required to approximate a graph __does not depend on the graph size__. We develop a new constructive version of the Weak Graph Regularity Lemma to efficiently construct an approximating ICG for any input graph. We then devise an efficient graph learning algorithm operating directly on ICG in linear memory and time with respect to the __number of nodes__ (rather than edges). This offers a new and fundamentally different pipeline for learning on very large non-sparse graphs, whose applicability is demonstrated empirically on node classification tasks and spatio-temporal data processing.

Poster
Mixture of Scales: Memory-Efficient Token-Adaptive Binarization for Large Language Models

Dongwon Jo, Taesu Kim, Yulhwa Kim, Jae-Joon Kim

展开摘要

Binarization, which converts weight parameters to binary values, has emerged as an effective strategy to reduce the size of large language models (LLMs). However, typical binarization techniques significantly diminish linguistic effectiveness of LLMs. To address this issue, we introduce a novel binarization technique called Mixture of Scales (BinaryMoS). Unlike conventional methods, BinaryMoS employs multiple scaling experts for binary weights, dynamically merging these experts for each token to adaptively generate scaling factors. This token-adaptive approach boosts the representational power of binarized LLMs by enabling contextual adjustments to the values of binary weights. Moreover, because this adaptive process only involves the scaling factors rather than the entire weight matrix, BinaryMoS maintains compression efficiency similar to traditional static binarization methods. Our experimental results reveal that BinaryMoS surpasses conventional binarization techniques in various natural language processing tasks and even outperforms 2-bit quantization methods, all while maintaining similar model size to static binarization techniques.

Poster
Span-Based Optimal Sample Complexity for Weakly Communicating and General Average Reward MDPs

Matthew Zurek, Yudong Chen

展开摘要

We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. For weakly communicating MDPs, we establish the complexity bound $\widetilde{O}\left(SA\frac{\mathsf{H}}{\varepsilon^2} \right)$, where $\mathsf{H}$ is the span of the bias function of the optimal policy and $SA$ is the cardinality of the state-action space. Our result is the first that is minimax optimal (up to log factors) in all parameters $S,A,\mathsf{H}$, and $\varepsilon$, improving on existing work that either assumes uniformly bounded mixing times for all policies or has suboptimal dependence on the parameters. We also initiate the study of sample complexity in general (multichain) average-reward MDPs. We argue a new transient time parameter $\mathsf{B}$ is necessary, establish an $\widetilde{O}\left(SA\frac{\mathsf{B} + \mathsf{H}}{\varepsilon^2} \right)$ complexity bound, and prove a matching (up to log factors) minimax lower bound. Both results are based on reducing the average-reward MDP to a discounted MDP, which requires new ideas in the general setting. To optimally analyze this reduction, we develop improved bounds for $\gamma$-discounted MDPs, showing that $\widetilde{O}\left(SA\frac{\mathsf{H}}{(1-\gamma)^2\varepsilon^2} \right)$ and $\widetilde{O}\left(SA\frac{\mathsf{B} + \mathsf{H}}{(1-\gamma)^2\varepsilon^2} \right)$ samples suffice to learn $\varepsilon$-optimal policies in weakly communicating and in general MDPs, respectively. Both these results circumvent the well-known minimax lower bound of $\widetilde{\Omega}\left(SA\frac{1}{(1-\gamma)^3\varepsilon^2} \right)$ for $\gamma$-discounted MDPs, and establish a quadratic rather than cubic horizon dependence for a fixed MDP instance.

Oral
Faster Accelerated First-order Methods for Convex Optimization with Strongly Convex Function Constraints

Zhenwei Lin, Qi Deng

展开摘要

In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$, regardless of the strong convexity of the constraint function. It is unclear whether the strong convexity assumption can enable even better convergence results. To address this issue, we have developed novel techniques to progressively estimate the strong convexity of the Lagrangian function. Our approach, for the first time, effectively leverages the constraint strong convexity, obtaining an improved complexity of $\mathcal{O}(1/\sqrt{\varepsilon})$. This rate matches the complexity lower bound for strongly-convex-concave saddle point optimization and is therefore order-optimal. We show the superior performance of our methods in sparsity-inducing constrained optimization, notably Google's personalized PageRank problem. Furthermore, we show that a restarted version of the proposed methods can effectively identify the optimal solution's sparsity pattern within a finite number of steps, a result that appears to have independent significance.

Poster
Constrained Latent Action Policies for Model-Based Offline Reinforcement Learning

Marvin Alles, Philip Becker-Ehmck, Patrick van der Smagt, Maximilian Karl

展开摘要

In offline reinforcement learning, a policy is learned using a static dataset in the absence of costly feedback from the environment. In contrast to the online setting, only using static datasets poses additional challenges, such as policies generating out-of-distribution samples. Model-based offline reinforcement learning methods try to overcome these by learning a model of the underlying dynamics of the environment and using it to guide policy search. It is beneficial but, with limited datasets, errors in the model and the issue of value overestimation among out-of-distribution states can worsen performance. Current model-based methods apply some notion of conservatism to the Bellman update, often implemented using uncertainty estimation derived from model ensembles. In this paper, we propose Constrained Latent Action Policies (C-LAP) which learns a generative model of the joint distribution of observations and actions. We cast policy learning as a constrained objective to always stay within the support of the latent action distribution, and use the generative capabilities of the model to impose an implicit constraint on the generated actions. Thereby eliminating the need to use additional uncertainty penalties on the Bellman update and significantly decreasing the number of gradient steps required to learn a policy. We empirically evaluate C-LAP on the D4RL and V-D4RL benchmark, and show that C-LAP is competitive to state-of-the-art methods, especially outperforming on datasets with visual observations.

Poster
The Empirical Impact of Neural Parameter Symmetries, or Lack Thereof

Derek Lim, Theo Putterman, Robin Walters, Haggai Maron, Stefanie Jegelka

展开摘要

Many algorithms and observed phenomena in deep learning appear to be affected by parameter symmetries --- transformations of neural network parameters that do not change the underlying neural network function. These include linear mode connectivity, model merging, Bayesian neural network inference, metanetworks, and several other characteristics of optimization or loss-landscapes. However, theoretical analysis of the relationship between parameter space symmetries and these phenonmena is difficult. In this work, we empirically investigate the impact of neural parameter symmetries by introducing new neural network architectures that have reduced parameter space symmetries. We develop two methods, with some provable guarantees, of modifying standard neural networks to reduce parameter space symmetries. With these new methods, we conduct a comprehensive experimental study consisting of multiple tasks aimed at assessing the effect of removing parameter symmetries. Our experiments reveal several interesting observations on the empirical impact of parameter symmetries; for instance, we observe linear mode connectivity between our networks without alignment of weight spaces, and we find that our networks allow for faster and more effective Bayesian neural network training.

Poster
Hamba: Single-view 3D Hand Reconstruction with Graph-guided Bi-Scanning Mamba

Haoye Dong, Aviral Chharia, Wenbo Gou, Francisco Vicente Carrasco, Fernando De la Torre

展开摘要

3D Hand reconstruction from a single RGB image is challenging due to the articulated motion, self-occlusion, and interaction with objects. Existing SOTA methods employ attention-based transformers to learn the 3D hand pose and shape, yet they do not fully achieve robust and accurate performance, primarily due to inefficiently modeling spatial relations between joints. To address this problem, we propose a novel graph-guided Mamba framework, named Hamba, which bridges graph learning and state space modeling. Our core idea is to reformulate Mamba's scanning into graph-guided bidirectional scanning for 3D reconstruction using a few effective tokens. This enables us to efficiently learn the spatial relationships between joints for improving reconstruction performance. Specifically, we design a Graph-guided State Space (GSS) block that learns the graph-structured relations and spatial sequences of joints and uses 88.5\% fewer tokens than attention-based methods. Additionally, we integrate the state space features and the global features using a fusion module. By utilizing the GSS block and the fusion module, Hamba effectively leverages the graph-guided state space features and jointly considers global and local features to improve performance. Experiments on several benchmarks and in-the-wild tests demonstrate that Hamba significantly outperforms existing SOTAs, achieving the PA-MPVPE of 5.3mm and F@15mm of 0.992 on FreiHAND. At the time of this paper's acceptance, Hamba holds the top position, Rank 1, in two competition leaderboards on 3D hand reconstruction.

Poster
Unlocking the Capabilities of Thought: A Reasoning Boundary Framework to Quantify and Optimize Chain-of-Thought

Qiguang Chen, Libo Qin, Jiaqi Wang, Jingxuan Zhou, Wanxiang Che

展开摘要

Chain-of-Thought (CoT) reasoning has emerged as a promising approach for enhancing the performance of large language models (LLMs) on complex reasoning tasks. Recently, a series of studies attempt to explain the mechanisms underlying CoT, aiming to deepen the understanding of its efficacy. Nevertheless, the existing research faces two major challenges: (1) a lack of quantitative metrics to assess CoT capabilities and (2) a dearth of guidance on optimizing CoT performance. Motivated by this, in this work, we introduce a novel reasoning boundary framework (RBF) to address these challenges. To solve the lack of quantification, we first define a reasoning boundary (RB) to quantify the upper-bound of CoT and establish a combination law for RB, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RBs. We further optimize these categories with combination laws focused on RB promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 27 models and 5 tasks, the study validates the existence and rationality of the proposed framework. Furthermore, it explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives. We hope this work can provide a comprehensive understanding of the boundaries and optimization strategies for reasoning in LLMs. Our code and data are available at https://github.com/LightChen233/reasoning-boundary.

Oral
Zipfian Whitening

Sho Yokoi, Han Bao, Hiroto Kurita, Hidetoshi Shimodaira

展开摘要

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are *uniform*; in reality, word frequencies follow a highly non-uniform distribution, known as *Zipf's law*. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective (Oyama et al., EMNLP 2023), and in terms of the loss functions for imbalanced classification (Menon et al. ICLR 2021). Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling (Mikolov et al., NIPS 2013), WhiteningBERT (Huang et al., Findings of EMNLP 2021), and headless language models (Godey et al., ICLR 2024), work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.

Poster
ImageNet3D: Towards General-Purpose Object-Level 3D Understanding

Wufei Ma, Guofeng Zhang, Qihao Liu, Guanning Zeng, Adam Kortylewski, Yaoyao Liu, Alan Yuille

展开摘要

A vision model with general-purpose object-level 3D understanding should be capable of inferring both 2D (*e.g.*, class name and bounding box) and 3D information (*e.g.*, 3D location and 3D viewpoint) for arbitrary rigid objects in natural images. This is a challenging task, as it involves inferring 3D information from 2D signals and most importantly, generalizing to rigid objects from unseen categories. However, existing datasets with object-level 3D annotations are often limited by the number of categories or the quality of annotations. Models developed on these datasets become specialists for certain categories or domains, and fail to generalize. In this work, we present ImageNet3D, a large dataset for general-purpose object-level 3D understanding. ImageNet3D augments 200 categories from the ImageNet dataset with 2D bounding box, 3D pose, 3D location annotations, and image captions interleaved with 3D information. With the new annotations available in ImageNet3D, we could (i) analyze the object-level 3D awareness of visual foundation models, and (ii) study and develop general-purpose models that infer both 2D and 3D information for arbitrary rigid objects in natural images, and (iii) integrate unified 3D models with large language models for 3D-related reasoning. We consider two new tasks, probing of object-level 3D awareness and open vocabulary pose estimation, besides standard classification and pose estimation. Experimental results on ImageNet3D demonstrate the potential of our dataset in building vision models with stronger general-purpose object-level 3D understanding. Our dataset and project page are available here: https://imagenet3d.github.io.

Poster
A Globally Optimal Portfolio for m-Sparse Sharpe Ratio Maximization

Yizun Lin, Zhao-Rong Lai, Cheng Li

展开摘要

The Sharpe ratio is an important and widely-used risk-adjusted return in financial engineering. In modern portfolio management, one may require an m-sparse (no more than m active assets) portfolio to save managerial and financial costs. However, few existing methods can optimize the Sharpe ratio with the m-sparse constraint, due to the nonconvexity and the complexity of this constraint. We propose to convert the m-sparse fractional optimization problem into an equivalent m-sparse quadratic programming problem. The semi-algebraic property of the resulting objective function allows us to exploit the Kurdyka-Lojasiewicz property to develop an efficient Proximal Gradient Algorithm (PGA) that leads to a portfolio which achieves the globally optimal m-sparse Sharpe ratio under certain conditions. The convergence rates of PGA are also provided. To the best of our knowledge, this is the first proposal that achieves a globally optimal m-sparse Sharpe ratio with a theoretically-sound guarantee.

Poster