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.

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Ensemble Learning Time Series Forecasting Non-Stationary Time Series Forecasting Electricity Load Forecasting Adaptive Learning Temporal Distribution Shift

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Abstract

Multi-Objective Optimization

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