433 research outputs found
MONISE - Many Objective Non-Inferior Set Estimation
This work proposes a novel many objective optimization approach that globally
finds a set of efficient solutions, also known as Pareto-optimal solutions, by
automatically formulating and solving a sequence of weighted problems. The
approach is called MONISE (Many-Objective NISE), because it represents an
extension of the well-known non-inferior set estimation (NISE) algorithm, which
was originally conceived to deal with two-dimensional objective spaces. Looking
for theoretical support, we demonstrate that being a solution of the weighted
problem is a necessary condition, and it will also be a sufficient condition at
the convex hull of the feasible set. The proposal is conceived to operate in
more than two dimensions, thus properly supporting many objectives. Moreover,
specifically deal with two objectives, some nice additional properties are
portrayed for the estimated non-inferior set. Experimental results are used to
validate the proposal and have indicated that MONISE is competitive both in
terms of computational cost and considering the overall quality of the
non-inferior set, measured by the hypervolume.Comment: 36 page
The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem
This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel, Iusem, and Svaiter [SIAM J. Optim., 15 (2005), pp. 953–970] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) approach for convergence analysis of the method is proposed where the first-order optimality condition of the scalarized problem is replaced by a necessary condition for weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.Fundação de Amparo à Pesquisa do Estado de GoiásConselho Nacional de Desenvolvimento CientÃfico e TecnológicoCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorMinisterio de EconomÃa y CompetitividadAgence nationale de la recherch
Multiobjective Reinforcement Learning for Reconfigurable Adaptive Optimal Control of Manufacturing Processes
In industrial applications of adaptive optimal control often multiple
contrary objectives have to be considered. The weights (relative importance) of
the objectives are often not known during the design of the control and can
change with changing production conditions and requirements. In this work a
novel model-free multiobjective reinforcement learning approach for adaptive
optimal control of manufacturing processes is proposed. The approach enables
sample-efficient learning in sequences of control configurations, given by
particular objective weights.Comment: Conference, Preprint, 978-1-5386-5925-0/18/$31.00 \c{opyright} 2018
IEE
Controllable Pareto Multi-Task Learning
A multi-task learning (MTL) system aims at solving multiple related tasks at
the same time. With a fixed model capacity, the tasks would be conflicted with
each other, and the system usually has to make a trade-off among learning all
of them together. For many real-world applications where the trade-off has to
be made online, multiple models with different preferences over tasks have to
be trained and stored. This work proposes a novel controllable Pareto
multi-task learning framework, to enable the system to make real-time trade-off
control among different tasks with a single model. To be specific, we formulate
the MTL as a preference-conditioned multiobjective optimization problem, with a
parametric mapping from preferences to the corresponding trade-off solutions. A
single hypernetwork-based multi-task neural network is built to learn all tasks
with different trade-off preferences among them, where the hypernetwork
generates the model parameters conditioned on the preference. For inference,
MTL practitioners can easily control the model performance based on different
trade-off preferences in real-time. Experiments on different applications
demonstrate that the proposed model is efficient for solving various MTL
problems
Pareto Multi-Task Learning
Multi-task learning is a powerful method for solving multiple correlated
tasks simultaneously. However, it is often impossible to find one single
solution to optimize all the tasks, since different tasks might conflict with
each other. Recently, a novel method is proposed to find one single Pareto
optimal solution with good trade-off among different tasks by casting
multi-task learning as multiobjective optimization. In this paper, we
generalize this idea and propose a novel Pareto multi-task learning algorithm
(Pareto MTL) to find a set of well-distributed Pareto solutions which can
represent different trade-offs among different tasks. The proposed algorithm
first formulates a multi-task learning problem as a multiobjective optimization
problem, and then decomposes the multiobjective optimization problem into a set
of constrained subproblems with different trade-off preferences. By solving
these subproblems in parallel, Pareto MTL can find a set of well-representative
Pareto optimal solutions with different trade-off among all tasks.
Practitioners can easily select their preferred solution from these Pareto
solutions, or use different trade-off solutions for different situations.
Experimental results confirm that the proposed algorithm can generate
well-representative solutions and outperform some state-of-the-art algorithms
on many multi-task learning applications.Comment: 33rd Conference on Neural Information Processing Systems (NeurIPS
2019), Vancouver, Canad
Explicit multiobjective model predictive control for nonlinear systems with symmetries
Model predictive control is a prominent approach to construct a feedback
control loop for dynamical systems. Due to real-time constraints, the major
challenge in MPC is to solve model-based optimal control problems in a very
short amount of time. For linear-quadratic problems, Bemporad et al.~have
proposed an explicit formulation where the underlying optimization problems are
solved a priori in an offline phase. In this article, we present an extension
of this concept in two significant ways. We consider nonlinear problems and --
more importantly -- problems with multiple conflicting objective functions. In
the offline phase, we build a library of Pareto optimal solutions from which we
then obtain a valid compromise solution in the online phase according to a
decision maker's preference. Since the standard multi-parametric programming
approach is no longer valid in this situation, we instead use interpolation
between different entries of the library. To reduce the number of problems that
have to be solved in the offline phase, we exploit symmetries in the dynamical
system and the corresponding multiobjective optimal control problem. The
results are verified using two different examples from autonomous driving
A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems
General multi-objective optimization problems are often solved by a sequence
of parametric single objective problems, so-called scalarizations. If the set
of nondominated points is finite, and if an appropriate scalarization is
employed, the entire nondominated set can be generated in this way. In the
bicriteria case it is well known that this can be realized by an adaptive
approach which, given an appropriate initial search space, requires the
solution of a number of subproblems which is at most two times the number of
nondominated points. For higher dimensional problems, no linear methods were
known up to now. We present a new procedure for finding the entire nondominated
set of tricriteria optimization problems for which the number of scalarized
subproblems to be solved is at most three times the number of nondominated
points of the underlying problem. The approach includes an iterative update of
the search space that, given a (sub-)set of nondominated points, describes the
area in which additional nondominated points may be located. In particular, we
show that the number of boxes, into which the search space is decomposed,
depends linearly on the number of nondominated points.Comment: 32 pages, 8 figures, Journal of Global Optimization, 201
Optimal Scalarizations for Sublinear Hypervolume Regret
Scalarization is a general technique that can be deployed in any
multiobjective setting to reduce multiple objectives into one, such as recently
in RLHF for training reward models that align human preferences. Yet some have
dismissed this classical approach because linear scalarizations are known to
miss concave regions of the Pareto frontier. To that end, we aim to find simple
non-linear scalarizations that can explore a diverse set of objectives on
the Pareto frontier, as measured by the dominated hypervolume. We show that
hypervolume scalarizations with uniformly random weights are surprisingly
optimal for provably minimizing the hypervolume regret, achieving an optimal
sublinear regret bound of , with matching lower bounds that
preclude any algorithm from doing better asymptotically. As a theoretical case
study, we consider the multiobjective stochastic linear bandits problem and
demonstrate that by exploiting the sublinear regret bounds of the hypervolume
scalarizations, we can derive a novel non-Euclidean analysis that produces
improved hypervolume regret bounds of . We
support our theory with strong empirical performance of using simple
hypervolume scalarizations that consistently outperforms both the linear and
Chebyshev scalarizations, as well as standard multiobjective algorithms in
bayesian optimization, such as EHVI.Comment: ICML 2023 Worksho
Topology of Pareto sets of strongly convex problems
A multiobjective optimization problem is simplicial if the Pareto set and
front are homeomorphic to a simplex and, under the homeomorphisms, each face of
the simplex corresponds to the Pareto set and front of a subproblem. In this
paper, we show that strongly convex problems are simplicial under a mild
assumption on the ranks of the differentials of the objective mappings. We
further prove that one can make any strongly convex problem satisfy the
assumption by a generic linear perturbation, provided that the dimension of the
source is sufficiently larger than that of the target. We demonstrate that the
location problems, a biological modeling, and the ridge regression can be
reduced to multiobjective strongly convex problems via appropriate
transformations preserving the Pareto ordering and the topology.Comment: 21 pages. Remarks 4.4 and 4.5 are added. A new application is given
in section 5.3. Introduction is also revised accordingl
A bi-criteria path planning algorithm for robotics applications
Realistic path planning applications often require optimizing with respect to
several criteria simultaneously. Here we introduce an efficient algorithm for
bi-criteria path planning on graphs. Our approach is based on augmenting the
state space to keep track of the "budget" remaining to satisfy the constraints
on secondary cost. The resulting augmented graph is acyclic and the primary
cost can be then minimized by a simple upward sweep through budget levels. The
efficiency and accuracy of our algorithm is tested on Probabilistic Roadmap
graphs to minimize the distance of travel subject to a constraint on the
overall threat exposure of the robot. We also present the results from field
experiments illustrating the use of this approach on realistic robotic systems.Comment: 19 pages, 12 figures; submitted for publication to IEEE Transactions
on Automation Science and Engineerin
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