Locally Adaptive Multi-Objective Learning

Jivat Neet Kaur; Isaac Gibbs; Michael I. Jordan

cs.LGFeb 16, 2026

Locally Adaptive Multi-Objective Learning

Authors: Jivat Neet Kaur, Isaac Gibbs, Michael I. Jordan

Organizations: University of California, Berkeley · Inria, Paris

Abstract

We consider the general problem of learning a predictor that satisfies multiple objectives of interest simultaneously, a broad framework that captures a range of specific learning goals including calibration, regret, and multiaccuracy. We work in an online setting where the data distribution can change arbitrarily over time. Existing approaches to this problem aim to minimize the set of objectives over the entire time horizon in a worst-case sense, and in practice they do not necessarily adapt to distribution shifts. Earlier work has aimed to alleviate this problem by incorporating additional objectives that target local guarantees over contiguous subintervals. Empirical evaluation of these proposals is, however, scarce. In this article, we consider an alternative procedure that achieves local adaptivity by replacing one part of the multi-objective learning method with an adaptive online algorithm. Empirical evaluations on datasets from energy forecasting and algorithmic fairness show that our proposed method improves upon existing approaches and achieves unbiased predictions over subgroups, while remaining robust under distribution shift.

Figures & tables

Panel of Figure 1 — Figure 1: GEFCom14-L electric load forecasting dataset. On the left hand side are the time series for the raw load (light brown) and temperature (light orange) data. The dark brown curves indicate the weekly (168-hourly) moving average. The shaded grey region shows the competition duration. On the right-hand side, we plot a weekly moving average of the local multiaccuracy error.

Figure 2: COMPAS dataset. Moving average of true recidivism over time. We show 30-day moving averages of

y

(recidivism indicator), computed overall and separately by racial group. For each calendar date, outcomes are first averaged across all individuals screened that day and then reported as a 30-day time-window rolling mean.

Figure 3: Local multiaccuracy error (left) and prediction error (right) on the GEFCom2014-L dataset. We skip the first ten time steps when plotting the multiaccuracy and prediction error for improved readability.

Figure 4: Local multiaccuracy error (left) and prediction error (right) on the COMPAS dataset. We skip the first two time steps when plotting the multiaccuracy error for improved readability.

Figure 5: Local multiaccuracy error on GEFCom2014-L for different interval widths. We skip the first thirty time steps when plotting the multiaccuracy error for improved readability.

Figure 6: Local multiaccuracy error on COMPAS for different interval widths. We skip the first two time steps when plotting the multiaccuracy error for improved readability.

Panel of Figure 7 — Figure 7: Local multiaccuracy error for different interval widths $\boldsymbol{|I|}$ , (a) GEFCom2014-L and (b) COMPAS. This is the same setting as Figure 5 and Figure 6 where we now show comparison with the adaptive objectives MA+pred algorithm.

Panel of Figure 8 — Figure 8: Total multiaccuracy error with varying interval width $\boldsymbol{|I|}$ , (a) GEFCom2014-L and (b) COMPAS. This is the same setting as Figure 5 and Figure 6 . We vary the window width $|I|$ used for the moving average of errors and plot the total multiaccuracy error under the curve.

	Objectives	Interpretation
Omniprediction	$\ell(p_{t}(x_{t}),y_{t})-\ell(f(x_{t}),y_{t})$	$p_{t}$ minimizes losses $\ell\in{\mathcal{L}}^{\prime}$ against competitor functions $f\in{\mathcal{F}}$
Multi-group learning	${\mathbbm{1}}\{x_{t}\in g\}(\ell(p_{t}(x_{t}),y_{t})-\ell(f(x_{t}),y_{t}))$	$p_{t}$ minimizes $\ell$ within groups $g\in{\mathcal{G}}$ against competitor functions $f\in{\mathcal{F}}$

Table 1: Examples of extensions of our general algorithm. We define the problem, set of objectives, and the interpretation of the objectives.

{\mathcal{L}}^{\prime}

denotes a finite class of losses.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 9: GEFCom2014-L: True load ( $y$ ) and constructed predictions $\tilde{p}_{t}$ . We plot the moving average of the binary $y$ over a window size $|I|=$ 336 hours (2 weeks) (top) and the baselines predictions $\tilde{p}_{t}$ constructed from the quantile forecasts using linear interpolation (bottom) over time.

Panel of Figure 10 — Figure 10: Total multiaccuracy error and prediction error with varying $\boldsymbol{m}$ , (a) GEFCom2014-L and (b) COMPAS. This is the same setting as Figure 3 and Figure 4 where we now vary the number of bins $m$ .

Panel of Figure 11 — Figure 11: Total multiaccuracy error with varying interval width $\boldsymbol{|I|}$ , (a) GEFCom2014-L and (b) COMPAS. This is the same setting as Figure 5 and Figure 6 . We vary the window width $|I|$ used for the moving average of errors and plot the total multiaccuracy error under the curve.

Panel of Figure 12 — Figure 12: Local multiaccuracy error with varying $\boldsymbol{\eta}$ for different interval widths $\boldsymbol{|I|}$ , (a) GEFCom2014-L and (b) COMPAS. This is the same setting as Figure 5 and Figure 6 where we now show results with different choices of $\eta$ in the locally adaptive MA+pred algorithm.

Panel of Figure 13 — Figure 13: Total multiaccuracy error with varying $\boldsymbol{\eta}$ and interval width $\boldsymbol{|I|}$ , (a) GEFCom2014-L and (b) COMPAS. This is the same setting as Figure 5 and Figure 6 . We vary the window width $|I|$ used for the moving average of errors and plot the total multiaccuracy error under the curve with different choices of $\eta$ in the locally adaptive MA+pred algorithm.

Panel of Figure 14 — Figure 14: Total multiaccuracy error for different $\tau$ with varying interval width $\boldsymbol{|I|}$ , (a) GEFCom2014-L and (b) COMPAS. This is the same setting as Figure 5 and Figure 6 . We vary the fixed width $\tau$ used for tuning MA+pred (locally adaptive) and the window width $|I|$ used for the moving average of errors and plot the total multiaccuracy error under the curve.

Panel of Figure 15 — Figure 15: Trajectories for (a) $\boldsymbol{\mu_{t}}$ and (b) $\boldsymbol{\beta_{t,0}}$ in the different jump shift settings. $\beta_{t,0}$ denotes the first coordinate of $\beta_{t}$ . $\beta_{t,j}$ is an affine transformation of $\mu_{t}$ by construction. Dashed vertical lines denote the boundaries between the regime switches where the size of the distribution shift changes.

Figure 16: Local multiaccuracy error in different jump shift settings, small (left), medium (mid), and large (right) jump shifts.

Multi-Objective Optimization

Multi-objective optimization studies how to find and choose solutions that balance competing goals, constraints, and preferences.

See all 266 papers

Optimal Recalibration of an Online Predictor
Jul 22, 2026Lunjia Hu, Kevin Tian, Chutong YangModel Calibration Online Calibration
Northeastern University · University of Texas at Austin
Instance-Adaptive Online Multiclass Multicalibration
Oct 11, 2026Zhiming Huang, Jamie Morgenstern, Aaron Roth +1Multicalibration Model Calibration
Paul G. Allen School of Computer Science and Engineering, University of Washington · Amazon · Department of Computer and Information Sciences, University of Pennsylvania
Hedging Memory Horizons for Non-Stationary Prediction via Online Aggregation
May 7, 2026Yutong Wang, Yannig Goude, Qiwei YaoEnsemble Learning Time Series Forecasting
Department of Statistics, LSE · Électricité de France R&D

Jul 22, 2026J/K move · Enter open · S save

Optimal Recalibration of an Online Predictor

Lunjia Hu, Kevin Tian, Chutong Yang

Northeastern University · University of Texas at Austin

Model Calibration Online Calibration

Open paper AskPDF arXiv

We study the problem of recalibrating an online predictor [KE17, OKS24]: given an arbitrary "hint" sequence of forecasts, the learner must output new predictions that are calibrated while incurring small excess error relative to the original forecasts, under a proper loss. We give an online algorithm that achieves

(\varepsilon, \varepsilon^2)

-recalibration for Lipschitz proper losses in

T \approx \varepsilon^{-3}

rounds, using an imbalanced extension of the recent simultaneous Blackwell approachability reduction framework of [HTY26]. We show that this tradeoff is optimal by proving a matching lower bound for recalibrating against the squared loss. We also prove a companion

\mathcal{K}_2

-recalibration theorem that obtains the same tradeoffs up to a logarithmic factor. As our main application, we show how our recalibration algorithms can be combined with the online refinement method of [FH23] to obtain simultaneous

\varepsilon

-calibration and

\varepsilon^2

-calibeating for smooth proper losses at the same asymptotic rate, improving upon prior works that achieved these properties separately or with a worse

\varepsilon

dependence. In particular, the

\mathcal{K}_2

variant answers a question of [CHJL26] on simultaneously achieving near-optimal calibeating and calibration rates. We also derive extensions to settings with multiple hint sequences. Finally, we empirically evaluate our algorithms on a classification dataset undergoing distribution shift.

Abstract

Multi-Objective Optimization

Explore similar work

Optimal Recalibration of an Online Predictor

Instance-Adaptive Online Multiclass Multicalibration

Hedging Memory Horizons for Non-Stationary Prediction via Online Aggregation