continuous optimization
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Controlled Text Generation as Continuous Optimization with Multiple Constraints
As large-scale language model pretraining pushes the state-of-the-art in text generation, recent work has turned to controlling attributes of the text such models generate. While modifying the pretrained models via fine-tuning remains the popular approach, it incurs a significant computational cost and can be infeasible due to a lack of appropriate data. As an alternative, we propose \textsc{MuCoCO}---a flexible and modular algorithm for controllable inference from pretrained models. We formulate the decoding process as an optimization problem that allows for multiple attributes we aim to control to be easily incorporated as differentiable constraints. By relaxing this discrete optimization to a continuous one, we make use of Lagrangian multipliers and gradient-descent-based techniques to generate the desired text. We evaluate our approach on controllable machine translation and style transfer with multiple sentence-level attributes and observe significant improvements over baselines.
DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks
This paper re-examines a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials. Next, focusing on a one-parameter-per-edge setting, it is shown that the Karush-Kuhn-Tucker (KKT) optimality conditions for the NOTEARS formulation cannot be satisfied except in a trivial case, which explains a behavior of the associated algorithm. We then derive the KKT conditions for an equivalent reformulation, show that they are indeed necessary, and relate them to explicit constraints that certain edges be absent from the graph. If the score function is convex, these KKT conditions are also sufficient for local minimality despite the non-convexity of the constraint. Informed by the KKT conditions, a local search post-processing algorithm is proposed and shown to substantially and universally improve the structural Hamming distance of all tested algorithms, typically by a factor of 2 or more. Some combinations with local search are both more accurate and more efficient than the original NOTEARS.
DAG Learning from Zero-Inflated Count Data Using Continuous Optimization
Sato, Noriaki, Scutari, Marco, Kawano, Shuichi, Yamaguchi, Rui, Imoto, Seiya
We address network structure learning from zero-inflated count data by casting each node as a zero-inflated generalized linear model and optimizing a smooth, score-based objective under a directed acyclic graph constraint. Our Zero-Inflated Continuous Optimization (ZICO) approach uses node-wise likelihoods with canonical links and enforces acyclicity through a differentiable surrogate constraint combined with sparsity regularization. ZICO achieves superior performance with faster runtimes on simulated data. It also performs comparably to or better than common algorithms for reverse engineering gene regulatory networks. ZICO is fully vectorized and mini-batched, enabling learning on larger variable sets with practical runtimes in a wide range of domains.
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DAGs with NO TEARS: Continuous Optimization for Structure Learning
Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: we formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree.
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Scaling Whole-body Multi-contact Manipulation with Contact Optimization
Levé, Victor, Moura, João, Fujita, Sachiya, Miyake, Tamon, Tonneau, Steve, Vijayakumar, Sethu
Daily tasks require us to use our whole body to manipulate objects, for instance when our hands are unavailable. We consider the issue of providing humanoid robots with the ability to autonomously perform similar whole-body manipulation tasks. In this context, the infinite possibilities for where and how contact can occur on the robot and object surfaces hinder the scalability of existing planning methods, which predominantly rely on discrete sampling. Given the continuous nature of contact surfaces, gradient-based optimization offers a more suitable approach for finding solutions. However, a key remaining challenge is the lack of an efficient representation of robot surfaces. In this work, we propose (i) a representation of robot and object surfaces that enables closed-form computation of proximity points, and (ii) a cost design that effectively guides whole-body manipulation planning. Our experiments demonstrate that the proposed framework can solve problems unaddressed by existing methods, and achieves a 77% improvement in planning time over the state of the art. We also validate the suitability of our approach on real hardware through the whole-body manipulation of boxes by a humanoid robot.
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Uncovering Gradient Inversion Risks in Practical Language Model Training
Feng, Xinguo, Ma, Zhongkui, Wang, Zihan, Chegne, Eu Joe, Ma, Mengyao, Abuadbba, Alsharif, Bai, Guangdong
The gradient inversion attack has been demonstrated as a significant privacy threat to federated learning (FL), particularly in continuous domains such as vision models. In contrast, it is often considered less effective or highly dependent on impractical training settings when applied to language models, due to the challenges posed by the discrete nature of tokens in text data. As a result, its potential privacy threats remain largely underestimated, despite FL being an emerging training method for language models. In this work, we propose a domain-specific gradient inversion attack named Grab (gradient inversion with hybrid optimization). Grab features two alternating optimization processes to address the challenges caused by practical training settings, including a simultaneous optimization on dropout masks between layers for improved token recovery and a discrete optimization for effective token sequencing. Grab can recover a significant portion (up to 92.9% recovery rate) of the private training data, outperforming the attack strategy of utilizing discrete optimization with an auxiliary model by notable improvements of up to 28.9% recovery rate in benchmark settings and 48.5% recovery rate in practical settings. Grab provides a valuable step forward in understanding this privacy threat in the emerging FL training mode of language models.
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